Please answer all parts of this question.

a) List the factors that affect the price of a put option. Discuss briefly how these factors will affect the price of a put option.

b) Derive the relationship between the values of the call and the put option on a non-dividend paying stock, with their exercise prices equal to the forward price of the stock. Assume that the no-arbitrage conditions are satisfied.

You own 5000 shares of stock Y. The current price of one share is 25 and the daily volatility of returns is 1.575%. The riskless interest rate (continuously compounded) is 10% and the stock pays no dividend. European call and put options on stock Y with an exercise price of 27 and maturities of 3 months and 9 months are traded in the market.

c) Consider a 9-month European call option on stock Y. Using a 3-period binomial tree

calculate the value of the call option in six months if, following good news regarding the Y

revenue outlook, the stock price increased during the first two periods.

d) A trading strategy consists of long positions on a 9-month European call option and a single 9-month European put option, both with a strike price of 27. Using a 3-step tree, calculate the strategy's cost at initiation and the maximum profit at expiration. Assume that the call option currently trades for 3.2 and that there are no arbitrage opportunities.

e) Assume now that the stock Y price is distributed log-normally such that you can use the Black-Scholes formula to price options on it. Calculate the value of a 3-month European put option with a strike price of 27? How many put or call options would you need to buy or sell to hedge the price risk of your long position is shares of stock Y? Are there any alternative strategies that could lead to the elimination of risk? How do they differ?