Question Financial Derivative Securities 312

Q Question 1 (4 marks)

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.

a) What is the price of the option if it is a European call?

b) What is the price of the option if it is an American call?

c) What is the price of the option if it is a European put?

d) Verify that put-call parity holds.

Question 2 (4 marks)

The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%. The risk-free rate is 4%. For a three-month time step: a) What is the percentage up movement?

b) What is the percentage down movement?

c) What is the probability of an up movement in a risk-neutral world?

d) What is the probability of a down movement in a risk-neutral world?

Use a two-step tree to value a six-month European call option and a six-month European put option. In both cases the strike price is $150.

Question 3 (3 marks)

A one year European put option and a one year European call option with a strike price of $59 are both priced at $5 in the market a one year futures price is currently traded at $58. The risk free rate is 7% per annum. Is there an arbitrage opportunity, if so, show the gain on the arbitrage.