The current price of firm A is $45. The yearly variance of returns is 15% and the CC yearly return is 10%. The CCIR risk free is 2%. Assume T=1 year. The stock does not pay dividends. Suppose there is a put option with strike price K=$50 and expiration T=1 year. If = 1, compute , , ,

a. Compute the price of a put option with yearly volatility=15% and expiration one year.

b. Using the binomial pricing model, compute the price of a put option with yearly volatility=20% and expiration one year. Hint: you need to compute first, u, d, q*. u 1.563948 d 0.639407 q 0.503778 q* 0.411874

c. What is the relationship between the put option price and the volatility using the binomial tree?

d. Using the Black-Scholes equation, compute the price of a put option with volatility 15% and expiration one year.

e. Using the Black-Scholes equation, compute the price of a put option with volatility 20% and expiration one year.

f. Compute the derivative of the option price using B-S with respect to the volatility. This is the Vega of the option!

g.a. Compute the price of a call option with volatility 15% and expiration one year.

h. Using the binomial pricing model, compute the price of a call option with volatility 20% and expiration one year. Hint: you need to compute again u,d,q,q*

i. What is the relationship between the put option price and the spot price using the binomial tree?

j. Using the Black-Scholes equation, compute the price of a call option with volatility 15% and expiration one year. The Black-Scholes formula is: 0 (1,0) (2,0)

k. Using the Black-Scholes equation, compute the price of a put option with volatility 20% and expiration one year. Compute the derivative of the option price using B-S with respect to the spot price. This is the Vega of the option!