Call option: A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset. Put option: It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset. Hedge ratio: A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range. To compute: The hedge ratio when the exercise price is $120 Determine the impact of more in the money on hedge ratio.

Question

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Answer 1

Question

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

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Students have asked these similar questions

Reconsider the determination of the hedge ratio in the two-state model, where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for the following exercise prices: (a) 120, (b) 110, (c) 100, (d) 90? (e) What do you conclude about the hedge ratio as the option becomes progressively more in the money?

Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state). What would be the call option hedge ratio for each of the following exercise prices: $135, $122, $111, $100, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state)? Exercise Price Hedge Ratio $135 ? $122 ? $111 ? $100 ?

Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state). Required: What would be the call option hedge ratio for each of the following exercise prices: $135, $127, $120, $115, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state)? What do you conclude about the hedge ratio as the option becomes progressively more in the money?

Answer 2

Question

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

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Answer 3

Question

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

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Answer 4

Question

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

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Answer 5

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

Answer 6

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Answer 7

Chapter 21, Problem 7PS

Summary Introduction

Call option:

A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

Determine the impact of more in the money on hedge ratio.

Answer 8

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

(a)

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $0=Cu=$120−$120 and the down value of call will be $0=Cd=$90−$120 , considering the exercise price of $120.

Given:

Cu=0Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=0$120−$90=0

Answer 13

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Answer 14

Summary Introduction

(b)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$110

Determine the impact of more in the money on hedge ratio.

Answer 15

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.33

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $10=Cu=$120−$110 and the down value of call will be $0=Cd=$90−$110 , considering the exercise price of $110.

Given:

Cu=$10Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$10−0$120−$90=0.333

Answer 20

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Answer 21

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$100

Determine the impact of more in the money on hedge ratio.

Answer 22

Expert Solution

Answer to Problem 7PS

The hedge ratio is

0.67

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $20=Cu=$120−$100 and the down value of call will be $0=Cd=$90−$100 , considering the exercise price of $100.

Given:

Cu=$20Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$20−0$120−$90=0.67

Answer 27

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.

Given:

Cu=$30Cd=0uS=$120dS=$90

Calculation:

Hedge ratio=Cu−CduS−dS=$30−0$120−$90=1

Answer 28

Summary Introduction

(D)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Hedge ratio:

A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.

To compute:

The hedge ratio when the exercise price is

$120

$110

$100

$90 and

Determine the impact of more in the money on hedge ratio.

Answer 29

Expert Solution

Answer to Problem 7PS

1

When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either $120=uS=$100×1.2 or $90=dS=$100×0.90 . After one year, the up value of call will be $30=Cu=$120−$90 and the down value of call will be $0=Cd=$90−$90 , considering the exercise price of $90.