A European call option on shares has 3 months to expiry. The exercise price of the option is $2.50, and the current price of the share is $3. The standard deviation of the share is 20% and the risk-free rate is 5%. Required: Calculate the value of the call option per share using the Black-Scholes formula.

A European call option on shares has 3 months to expiry. The exercise price of the option is $2.50, and the current price of the share is $3. The standard deviation of the share is 20% and the risk-free rate is 5%. Required: Calculate the value of the call option per share using the Black-Scholes formula.

Fundamentals of Financial Management (MindTap Course List)

14th Edition

ISBN:9781285867977

Author:Eugene F. Brigham, Joel F. Houston

Publisher:Eugene F. Brigham, Joel F. Houston

Chapter18: Derivatives And Risk Management

Section18.A: Valuation Of Put Options

Problem 1P

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V3. Consider a European call option on Allana Inc. stock. The option matures in 8 months and its strike price is $50. Current stock price per Allana Inc.’s share is $50. Allana Inc. will pay $2 dividend per share in 2 month and $3 per share in 6 months and the risk free rate is 3% per annum with continuous compounding for all maturities. Assume that the standard deviation of Allana Inc.’s stock return is 30% per year. The Black-Scholes value of this call option is ______. $18.31 $15.17 $6.92 $5.24 $2.96
Q5. Consider a six-month European put option on a non- dividend-paying stock. The current stock price is $100 and the strike price is $105. The risk-free rate is 10% per annum with semiannual compounding. A lower bound for the price of the European put option is $ _ If the put option were an American put option, a lower bound would be $_ Q6. The price of a European call that expires in six months and has a strike price of $50 is $2. The current underlying stock price is $50, and a dividend of $2 is expected in three months from now. The risk-free interest rate is 10% per annum with quarterly compounding. For the same stock, what is the price of a European put option with the same maturity and strike price? $ Q7. Suppose that c1, c2, and c3 are the prices of European call options on a particular stock with strike prices K1, K2, and K3, respectively, and that p1, p2, and p3 are the prices of European put options on the same stock with strike prices K1, K2, and K3, respectively, where K…
3. Consider a European put option on a non-dividend paying stock with exercise price 100 USD and expiration in one month. Interest rate is 1 percent and volatility of the stock is 0.4. Stock price 90 USD. Option price?? Use excel.
Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.
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D6) You use the Black Scholes model to price a Call option on a stock with discrete dividends. The dividends will be given in months 1, 5, and 9, each 3 USD. The current value of the stock is 105 USD, the strike price is 90 USD, the continuously compounded annual risk-free rate is 0.05, the volatility is 0.08, the time to maturity is 12 months. Calculate the price of the option.
37. A European put option with an exercise price of $100 and 3 months till maturity is trading at $4 when the underlying stock is trading at $97.The risk free rate equals 5%. All other factors remaining same, the value of an American put option is least likely: a.$3 b.$4 c.$4.05
V4. Using a two-step binomial tree, calculate the value of an American call option where the underlying stock pays a dividend of $1 per share just before the option’s expiration. The stock is trading at $22, the strike is $20, the risk-free rate is 4%. The option is outstanding for another two years (each step in the binomial tree is one year long). The stock is expected to rise or fall 10% in each one-year period prior to expiry. Can you please explain/show in Excel including formulas.
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