. (Pricing Call Options) Consider a l-period binomial model with R = 1.05, So = 50, u = 1/d = 1.08. What is the value of a European call option on the stock with strike K = 52, assuming that the stock does not pay dividends? Please submit your answer rounded to two decimal places. So for example, if your answer is 5.489 then you should submit an answer of 5.48 or 5.49.

. (Pricing Call Options) Consider a l-period binomial model with R = 1.05, So = 50, u = 1/d = 1.08. What is the value of a European call option on the stock with strike K = 52, assuming that the stock does not pay dividends? Please submit your answer rounded to two decimal places. So for example, if your answer is 5.489 then you should submit an answer of 5.48 or 5.49.

Financial Management: Theory & Practice

16th Edition

ISBN:9781337909730

Author:Brigham

Publisher:Brigham

Chapter8: Financial Options And Applications In Corporate Finance

Section: Chapter Questions

Problem 5MC: In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1)...

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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
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 3.7739. and put option value is 1.8101 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. c. What would be the extent of your profit in (a) depend on?
Suppose there is also a 1-year European put option on the same stock as in Question 3 with exercise price $30. The current stock price is also $25 and the stock price, in 1 year, will be either $35 (up by 40%) or $20 (down by 20%). The interest rate is 8%. This stock does not pay dividend. What is the value of the put option? Please use risk neutral probability method and assume discrete discounting. (2) What is put-call parity in option pricing? What needs to be true in order for put-call parity to hold?
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?
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.
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?
d. Briefly explain why you would pay more for a European call option ona (non-dividend paying) stock which has an annual return volatility of50% than for a European call on a (non-dividend paying) stock thathas annual volatility of 10% (assuming that all other variables thataffect option prices are the same for the two options.)
Consider a European call on Procter and Gamble stock (PG) that expires in one period. The current stock price is $120, the strike price is $130, and the risk-free rate is 5%. Assume that PG stock will either go up to $150 (probability = .4), or go down to $90 (probability = .6). Construct a replicating portfolio based on shares of PG stock and a position in a risk-free asset, and compute the price of the call option.
1. What is the fair value for a two-year American put option with a strike price of $85 over a stock which is trading at $86.15 which has a volatility of 37% when the risk free rate is 1.75% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of a down movement in this stock? c) What is the probability of an up movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the call option with the same strike price?
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.
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.