EXTENSIONS OF OPTION PRICING

All the option pricing models described so far—the binomial, the Black-Scholes, and the jump process models—are designed to value options with clearly defined exercise prices and maturities on underlying assets that are traded. However, the options we encounter in investment analysis or valuation are often on real assets rather than financial assets. Categorized as real options, they can take much more complicated forms. This section considers some of these variations.

Capped and Barrier Options

With a simple call option, there is no specified upper limit on the profits that can be made by the buyer of the call. Asset prices, at least in theory, can keep going up, and the payoffs increase proportionately. In some call options, though, the buyer is entitled to profits up to a specified price but not above it. For instance, consider a call option with a strike price of K₁ on an asset. In an unrestricted call option, the payoff on this option will increase as the underlying asset's price increases above K₁. Assume, however, that if the price reaches K₂, the payoff is capped at (K₂ - K₁). The payoff diagram on this option is shown in Figure 5.5.