DER 06 Option valuation
The standard assumptions regarding option valuation were introduced by Black/Scholes (1973) and Merton (1973). They assume that the security underlying the option follows geometric Brownian motion with constant mean and variance. That implied that the security has a lognormal price distribution at the option's expiration. They also assume that a risk-free hedge may be formed between the option and its underlying security.
Valuing an option relative to its underlying benchmark requires an assumption about the benchmark’s price distribution. Under the assumption that the benchmark’s price distribution is lognormally distributed, many valuation results may be derived. One such valuation result is the infamous Black-Scholes European-style option valuation formula.
DER 06.2 Option valuation: Binomial method
Some options, because of their contract design, do not have analytical valuation formulas (e.g., American-style options). Nonetheless, they can be valued accurately using approximations. The most popular among these is the binomial method.
Some options are written on the prices of more than one asset. Most of them do not have analytical valuation formula. Nonetheless, they can be valued accurately using approximations. The most versatile of these is Monte Carlo simulation.
The importance of option valuation is not driven solely by the desire to identify mispriced options. Its greatest value lies in providing managers with the ability to measure risk exposures.