You are attempting to value a call option with an exercise price of $55 and one year to expiration. The underlying stock pays no dividends, its current price is $55, and you believe it has a 50% chance of increasing to $85 and a 50% chance of decreasing to $25. The risk-free rate of interest is 6%. Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Value of the call

You want to buy a stock that is currently selling for $40. You forecast that in one year, the stocks price will be either $102 or $4, with equal probabilities. There is a one-year call option on the stock available with an exercise price of $80. You are able to borrow at a rate of 6.50%. You would like to hedge your stock position using the call option.

a. What will be the calls value if the stock price is $102 in one year? What will be the calls value if the stock price is $4 in one year? (Round your answers to the nearest dollar.)

Call value at $102	$
Call value at $4	$

b. What is the hedge ratio you should use? (Round your answer to 4 decimal places.)

Hedge ratio

c. Assume that you can purchase fractional shares of stock. How many shares of stock would you buy? (Round your answer to 4 decimal places.)

Shares

Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.)

Stock price	$	59
Exercise price	$	56
Interest rate		7	%
Dividend yield		4	%
Time to expiration		0.50
Standard deviation of stocks returns		28	%

Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $63.50 currently and pays an annual dividend of $1.77. The standard deviation of the stocks returns is 0.19 and risk-free interest rate is 4.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.)

Put value

Calculate the elasticity of a call option with a premium of $4.00 and a strike price of $65. The call has a hedge ratio of 0.7, and the underlying stocks price is currently $55. (Round your answer to 2 decimal places.)

Elasticity of the call %