1. Figure 12.1. Call price as a function of the stock price

2. Figure 12.2. Hedge ratio of Black-Scholes call as the price of the stock changes

3. Figure 12.3. Performance of the delta hedge

4. Figure 12.4. Stock price paths. of a stock price that is lognormally distributed

5. Figure 12.5. Vega as a function of the stock price for a call option with exercise price of 50 and a volatility of 20%

6. Figure 12.6. Price of put as a function of the stock price

7. Figure 12.7. Hedge ratio of put

8. Figure 12.8. Put price as a function of time to maturity and stock price

9. Figure 12.9. Typical smile before the crash of 1987

10. Figure 12.10. Typical smile after the crash of 1987