- Growth in Structured Securities
- Growing Emphasis on Low Volatility and Dividends
- Criticisms of Structured Securities
- Demand for Quantitative Skills
- Direction of Quantitative Finance
- When I Realized It Might Be Easier
- Try Again
- The Spreadsheet
- Visualizing the Result
- What It Means and Why It Works: A Nontechnical Overview
- It Doesn't Get Too Complicated
- An Integrated View of Risk Management
Visualizing the Result
Figure 1.2 is a graph of the spreadsheet. The call option payoffs are shown on the right side of the graph, and the values for these payoffs are on the right axis. The probabilities of the payoffs are shown as the normal distribution curve. The probability values are on the left axis.
Figure 1.2. Stock option payoffs with probabilities
The option price is the weighted average option payoff, where the weights are the probabilities. In other words, this is Column E (the option payoff) times Column B (the corresponding probabilities), or as shown here in Figure 1.3.
Figure 1.3. Weighted stock option payoffs
The middle section is the curve representing the option price. The sum of these values is equal to the option price. The relative height of the curve shows which stock prices contribute most to its value. In this view, even though the payoff grows large on the right side, the probabilities of those payoffs are growing smaller at a even faster rate, so high payoffs contribute relatively less than payoffs closer to the center of the graph.