• A non-dividend paying stock currently trades for $42 and has an annualised return volatility (standard deviation) of 20%. Given that the continuously compounded risk-free rate of return is 5% p.a., complete the following:
• a. Using a two-step binomial tree, price the European put option on the stock when the put has an exercise price of $40 and 6 months to maturity.
• (4 marks)
• b. Using the Black-Scholes-Merton Model, price the put option from part a) above.
• (3 marks)
• c. What is the delta of the put option from part b) under the Black-Scholes-Merton Model? How can a long position in 1000 of these put options be made delta neutral using the underlying stock? What would you have to do to delta hedge the position over the next 6 months?
• (3 marks)
• d. Explain a way that you can hedge some of the downside risk (i.e. the risk of future losses) of a stock holding using options, without paying any option premium. State clearly what options you buy or write and which have higher/lower strike prices.