Problem:

a) Write down and explain the Black-Scholes European call option pricing formula. Discuss how call prices it delivers change with each of the inputs to the calculation.

b) What is the price of a European call option on a non-dividend paying stock when the stock price is $52, the strike price is $50 and the risk-free rate is 12% per annum, the volatility is 30% per annum and the time to maturity is three months?

c) A call option with a strike price of $50 costs $2. A put option with a strike price $45 costs $3. Explain, using an appropriate diagram, how a strangle can be created from these two options. What is the pattern of profits from the strangle?

d) A one month European put option on a non-dividend paying stock is currently selling for $ 2.50. The stock price is $47, the strike price is $50 and the risk free interest rate is 6% per annum. What opportunities are there for an arbitrageur?