Two different European GM call options are available in the market. Option A has an exercise price of $95, trades at an implied annual volatility of 30% and costs $3.7521 per call. Option B has a strike price of $85, trades at an implied annual volatility of 20% and costs $7.2748 per call. Both options are based on the same stock which is currently trading at $90 and pays no dividends. The annual risk free rate is 5%. Both option prices are right in line with a Black-Scholes valuation.
a) You believe that all GM call option volatility is going to converge to 25% in the short term. Given this, set up a delta neutral strategy using these two options to take advantage of the convergence. Assume you want to trade 1,000 Option A calls.
b) Estimate the profit if the convergence happens immediately and the stock price stays at $90.
c) What is the profit if the stock moves to $89 or to $91? How well is the hedge performing?