Exercise 8.3 An important part of the argument that leads to the Black-Scholes PDE is the assumption of replication. We assume that we can per- fectly replicate the call option by forming a portfolio wherein we continuously trade between the stock and the riskless money market. If C = h(t,S) is the price of the call option, S is the stock price, and N=-A is the number of shares of stock held in the portfolio, then this means that C+N-S= h(t,S) - ACS (8.11) is instantaneously risk-free. We saw that Ito's formula and the con- cept of no arbitrage yield that Acom (8.12) The same argument holds for a European put option; in that case, (8.13) 4P _ ah? 1. Compute AC using (8.4). 2. Compute AP using (8.10). 3. Comment on the signs of AC and AP. What does it mean if AC or AP is negative? Positive? Exercise 8.3 An important part of the argument that leads to the Black-Scholes PDE is the assumption of replication. We assume that we can per- fectly replicate the call option by forming a portfolio wherein we continuously trade between the stock and the riskless money market. If C = h(t,S) is the price of the call option, S is the stock price, and N=-A is the number of shares of stock held in the portfolio, then this means that C+N-S= h(t,S) - ACS (8.11) is instantaneously risk-free. We saw that Ito's formula and the con- cept of no arbitrage yield that Acom (8.12) The same argument holds for a European put option; in that case, (8.13) 4P _ ah? 1. Compute AC using (8.4). 2. Compute AP using (8.10). 3. Comment on the signs of AC and AP. What does it mean if AC or AP is negative? Positive