Calculate the value of a call option for the following stock. Use the Black-Scholes formula. Time to expiration Standard deviation Exercise price Stock price Annual interest rate. Dividend 6 months 50% per year $50 Value of a call option $50 3% 0 (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Problem 1. Assume that the interest rate is 5%, contimuously compounded annually, and consider call and put options of both American and European style expiring in 6 months on non-dividend paying stock. For each of the following scenarios, check if you can find an arbitrage opportunity and, if you can, describe it: (i) The strike price of a European put option is $3 and the option is traded at $4. (ii) The shares are traded at $3 and the American call option is traded at $3.20.

Use the Black-Scholes formula for the following stock: Time to expiration 6 months Standard deviation 60% per year Exercise price $57 Stock price $57 Annual interest rate 3% Dividend 0 Recalculate the value of the call with the following changes: a. Time to expiration 3 months b. Standard deviation 25% per year c. Exercise price $64 d. Stock price $64 e. Interest rate 6% Select each scenario independently. Note: Round your answers to 2 decimal places.

D4) Finance Calculate the price of a 3-month American put option on a non-dividend-paying stock when the stock price is $50, the strike price is $50, the risk-free interest rate is 5% per annum, and the volatility is 25% per annum. Use a binomial tree with a time interval of 1 month.