Question 3.Consider a European option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, continuously compounded risk-free interest rate is 5%, volatility is 25% per annum, and time to maturity is 4 months (assume 4 months is equal to 120 days).

1. Find the value of a call option at the strike price of $29 using the Black-Scholes option pricing model. Show all steps. (8)
2. Find the value of a put option at thestrike price of $29 using the Black-Scholes option pricing model. Show all steps. (8)
3. Show that put-call parity holds using the put and the call at thestrike price of $29. (you need to find the value of both sides of the put-call parity for this.) (8)

Question 4.Consider the same options as in question 3 and answer the following.

1. Find values of Delta for the two options. (5)
2. Using just delta,what should be the change in theprice of the call option if theprice of the underlying stock increases by $0.04?(5)
3. Briefly explain in words why thevalue of delta for a long call is between 0 and 1.(4)
4. Find values of Theta for the two options. (6)
5. What is the effect of theta on a long call option? (4)