1. A call option is written with a strike price $40 for the purchase of 100 shares of a stock. Current stock price is $40, volatility on an annual basis is 30% (252 business days) and r=8% on an annual basis. Maturity is set at 91 days. Delta hedge the option on Day 0 and Day1. Assume that the actual stock price on Day 1 is $40.5 and on Day 2 is $39.25. Calculate the profit of a portfolio with one long position with shares of the underlying asset and one short position on the stock call option after hedging on Day. What is the lim t -> T delta (t) for this option?
2. Back to problem 5: If I sell the option on Day 1 at the risk-free price what should be its sale price? Find the value of the portfolio on Day 2. Although we sold the option on Day 1, we still value the portfolio as if the call option is not sold (to distinguish the role of the delta shares from the option we use the terms long and short for the delta shares and the option respectively). We do this because we gradually build the value required for closing out the portfolio on the maturity day.