Assume S0 = K =102 and all options have an expiration date on 28th October.

The call and put premia are P = 3 and C = 5. Explain the payoffs, profits, and breakeven stock prices for a long straddle. Clearly set out the payoffs in an appropriate figure. Why would this strategy be useful (you can use an example)? 

 

(b) A down-and-out put (on a stock) has K=100, T=1, r=5%pa and the barrier is L=90. The current stock price is S=100, the volatility of the stock is 20%pa and the stock price's expected growth rate is μ = 10% pa. Assume the stock price is monitored daily.

 

(i)  Carefully set out the steps required to price a down-and-out put using Monte Carlo Simulation, MCS. (You may use illustrative figures/diagrams in your answer). 

(ii)  Explain how you assess the accuracy of the option price (from the MCS) and how you could improve the accuracy. 

 

(c) You run a gas fired power station, which sells electricity to the national grid, at a fixed price. Explain the use of energy derivatives in hedging the "price risk".