The value by which a contract is mispriced with the help of given information. Introduction: Future contract : It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

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Answer 1

Question

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

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Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?

The S&P portfolio pays a dividend yield of 1% annually. Its current value is 1,300. The T-billrate is 4%. Suppose the S&P futures price for delivery in 1 year is 1,330. Construct an arbitragestrategy to exploit the mispricing and show that your profits 1 year hence will equal the mispricing in the futures market.

A non-dividend-paying stock has a current price of 800 ngwee. In any unit of time (t, t + 1) the price of the stock either increases by 25% or decreases by 20%. K1 held in cash between times t and t + 1 receives interest to become K1.04 at time t + 1. The stock price after t time units is denoted by St.Required:I. Calculate the risk-neutral probability measure for the model.II. Calculate the price (at t = 0) of a derivative contract written on the stock with expiry date t = 2 which pays 1,000 ngwee if and only if S2 is not 800 ngwee (and otherwise pays 0).

Answer 2

Question

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

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Answer 3

Question

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

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Answer 4

Question

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

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Answer 5

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

Answer 6

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

Answer 7

Chapter 23, Problem 25PS

a.

Summary Introduction

To compute: The value by which a contract is mispriced with the help of given information.

Introduction:

Future contract: It is supposed to be a legal agreement required to purchase or sell a commodity or asset in the future. This contract will specify the price at which the purchase or sale of the commodity or asset should be done at a specified time which will be agreed by the parties in advance.

Answer 8

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

Answer 9

b.

Summary Introduction

To prepare: A zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

Introduction:

Zero-net investment arbitrage strategy: According to this startegy, the securities should be purchased or sold in such a manner that the net result i.e., net investment becomes zero.

Answer 10

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

Answer 11

c.

Summary Introduction

To evaluate: The existence of arbitrage opportunity assuming the short sales of the stock in market index and the income is not received.

Introduction:

Arbitrage opportunity: It is an opportunity which can be availed to make a risk-free profit even in market fluctuations. The process of arbitrage involves buying of an asset in one market with a lesser price and sell it another market with a higher price.

Answer 12

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

Answer 13

d.

Summary Introduction

To compute: The no-arbitrage band for the stock-futures price relationship. Given stock index of 1900.

Introduction:

No-arbitrage: No-arbitrage can also be called as arbitrage- free principle. According to this principle, the price of the derivative is fixed in such a way that no one involved in trading can make a risk-free profit by purchasing one and selling the other.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 23 - Prob. 1PS Ch. 23 - Prob. 2PS Ch. 23 - Prob. 3PS Ch. 23 - Prob. 4PS Ch. 23 - Prob. 5PS Ch. 23 - Prob. 6PS Ch. 23 - Prob. 7PS Ch. 23 - Prob. 8PS Ch. 23 - Prob. 9PS Ch. 23 - Prob. 10PS

Solution Summary: The author describes a zero-net-investment arbitrage portfolio to show that riskless profits can be equalized to futures mispricing.

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