Problem 1) A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 12% or fall by 12%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 3%. What is the risk-neutral probability of a 12% rise in both quarters?
Problem 2) A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 12% or fall by 12%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 3%. What is the value of the call option?
Problem 3) A stock price is $30, the expected return is 18% per annum and the volatility is 20% per annum. What is the standard deviation of the logarithm of the stock price in two years?
Problem 4) A stock price is $30, the expected return is 18% per annum and the volatility is 20% per annum. What is the lower 95% confidence limit for the logarithm of the stock price in two years?
Problem 5) For a call option on a non-dividend paying stock, the strike price is $40, the stock price is $37.65, the risk-free rate is 4% per annum, the volatility is 40% per annum and the time to maturity is 6 months. What is the price of the call option?
Problem 6) A portfolio of derivatives on a stock has a delta of -1200 and a gamma of -200. What position in the stock in the stock would create a delta-neutral portfolio
Problem 7) The delta of a European call option on a non-dividend paying stock is 0.4, its gamma is 0.08 and its vega is 0.2. What is the delta of a European put option with the same strike price and time to maturity as the call option?