A European Call Option has 3 months till maturity, an exercise price of $200, a spot price of $200, and the stock price volatility is 40% p.a.. The risk free interest rate is 6% p.a. continuously compounded. The stock pays no dividend during the term of the option.

(i) Use the black scholes formula to compute the price of the call option. Show your working to compute the values of 1 d , 2 d , and C

(ii) Compute the value of a forward contract to buy the stock in 3 months for the same exercise price as for the call

(iii) Use the put call parity relationship to compute the price of a put option with the same details as the above call option

(iv) A straddle is an option trading strategy where you buy a call and a put over the same stock with the same maturity date, same exercise price etc. Compute the cost of the straddle created with the call and put options above

(v) Suppose you buy the straddle combination of options as in (iv) and the following day, an event occurs that increases the volatility of the stock underlying the option but doesn't change the price of the stock. What effect would this have on the value of the straddle combination of options? Would the value go up or go down? Give a reason why.