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Problem -
a) You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120.00 and a 50% chance of decreasing to $80.00. The risk-free rate of interest is 10%. Calculate the call options value using the two-state stock price model.
b) Consider an increase in the volatility of the stock in the previous problem. Suppose that if the stock increases in price, it will increase to $130 and then if it falls, it will fall to $70.00. Show that the value of the call option is now higher than the value derived in the previous problem.
c) Calculate the value of a put option with exercise price $100 using the data in this problem. Show that the put call parity theorem is satis?ed in your solution.
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