Afinancial option is a security that grants its owner the right, but not the obligation, to trade another financial security at specified times in the future for an agreed amount. The financial security that can be traded in the future is called the underlying asset, or simply the underlying. An option is an example of a derivative security, so named because its value is derived from that of the underlying. Placing a value on an option is made difficult by the asymmetric payoff that arises from the option owner’s right to trade the underlying in the future if doing so is favorable, but to avoid trading when doing so is unfavorable.
Options allow for hedging against one-sided risk. However, a prerequisite for efficient management of risk is that these derivative securities are priced correctly when they are traded. Nobel laureates Fischer Black, Robert Merton, and Myron Scholes developed in the early 1970s a method to price specific types of options exactly, but their method does not produce exact prices for all types of options. In practice, Monte Carlo simulation is often used to price derivative securities. In this chapter we see how to use Crystal Ball for option pricing.
The optionality leads to a nonlinear payoff that is convolved with the lognormally distributed stock price to result in a probability distribution for option value that is difficult for many analysts to visualize without Crystal Ball. The payoff diagrams familiar to options traders ...