CHAPTER 12 Financial Options A financial 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. | u12 Financial Options A financial 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. The problem of 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. This chapter shows how to use Crystal Ball for option pricing. The optionality leads to a nonlinear payoff that is convolved with the log-normally 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 give the range and level of option value as a function of stock price but don t offer insights into the probabilities associated with payoffs. However Crystal Ball forecasts do this readily. The next section provides brief background material on financial options. For more information consult the books by Hull 1997 McDonald 2006 or Wilmott 1998 2000 . TYPES OF OPTIONS Denote the price of the underlying asset by St for 0 t T where T is the expiration date of the option. The agreed amount for
