Write down the formula for:fa) price of an European put optionf6) price of a European calli optionKoth on a non-dividend paying stock andKoth derived from the Black-Scholes-Merton Differential EquationsDefine every symbol in the formulae.Given that, with the usual notation,S, = 42,K = 40,r3D0.1, о %3D0.2, Т%3D0.5N(0.7693)N(0.6298) = 0.73400.77914.79Calculate the price of a European call option on the stock.Consider an option on a dividend paying stock with thefollowing characteristicss, = $30Going ex-dividend in 1.5 months.Expected Dividend is $0.5Exercise Price is $29.Risk free rate is 5% per annumVolatility is 25% per annumTime to maturity is 4 monthsCalculate price if(a) European Call(b) European Put2.522.52Given furtherN (.3068)= 0.6205N (.1625) = 0.5645

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Write down the formula for: fa) price of an European put option fb) price of a European call option both on a non-dividend paying stock and Koth derived from the Black-Scholes-Merton Differential Equations Define every symbol in the formulae. Given that, with the usual notation, S, = 42, K = 40, r= 0.1, ơ =0.2, T = 0.5 N(0.7693) = 0.7791 N(0.6298) = 0.7340 4.78

Write down the formula for: fa) price of an European put option fb) price of a European call option both on a non-dividend paying stock and Koth derived from the Black-Scholes-Merton Differential Equations Define every symbol in the formulae. Given that, with the usual notation, S, = 42, K = 40, r= 0.1, ơ =0.2, T = 0.5 N(0.7693) = 0.7791 N(0.6298) = 0.7340 4.78

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain
2. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model. 3Suppose a European put options has a price higher than that dictated by the putcall parity.a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question 2 above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?
Consider an european call option on a stock that is not paying dividends with the following characteristics. (i) The stock price at t = 0 is S = $30. (ii) The stricke price is $31. (iii) The volatility of the stock is 20%. (iv) The free risk interest rate is 7%. Construct a 2 period recombining Binomial tree diagram and specty tne varue or the can optron at eacn node of the tree diagram.
Suppose you want to price an American style put option for a stock being traded on theKuispad Stock Exchange having the following parameters: s = 18, t = 0.25, K = 20, σ = 0.2, r = 0.07. Using n = 5, calculate the value of V0(0). Provide all necessary details
Consider a 11-period binomial model with R=1.02, S0 = 100, and u= 1.05. Compute the value of a European call option on the stock with strike K = 102. The stock does not pay dividends.
Consider a 11-period binomial model with R=1.02, S0 = 100, and u= 1.05. Compute the value of a European call option on the stock with strike K = 102. The stock does not pay dividends. (Note - the correct answer is neither $2.06 or $1.76)
Let C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?
Suppose you want to price an American style put option for a stock being traded on theDryfontein Stock Exchange having the following parameters: s = 18, t = 0.25, K = 20, σ =0.2 and r = 0.07. Using n = 5, calculate the value of V2(2). Provide all necessary details.
1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.
In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held untilmaturity. Under what circumstances will the holder of the option make a profit? Underwhat circumstances will the option be exercised? Draw a diagram illustrating how the profitfrom a long position in the option depends on the stock price at maturity of the option. Suppose that a European put option to sell a share for $60 costs $8 and is held untilmaturity. Under what circumstances will the seller of the option (the party with the shortposition) make a profit? Under what circumstances will the option be exercised? Draw adiagram illustrating how the profit from a short position in the option depends on thestock price at maturity of the option.

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