44 - Options II: Pricing and valuation

Abstract

This chapter reviews the parameters used in the pricing of an option and introduces the Black–Scholes model and binomial model. Pricing an option is a function of the probability that it will be exercised. Essentially the premium paid for an option represents the buyer's expected profit on the option. One of the key assumptions made by the Black–Scholes model (B–S) is that asset prices follow a lognormal distribution. The distribution of prices is called a lognormal distribution because the logarithm of the prices is normally distributed; the asset returns are defined as the logarithm of the price relatives and are assumed to follow the normal distribution. An option pricing model calculates the option price from volatility and other parameters. Used in reverse the model can calculate the volatility implied by the option price. Volatility measured in this way is called implied volatility. Most option pricing models are based on one of two methodologies, although both types employ essentially identical assumptions. The first method is based on the resolution of the partial differentiation equation of the asset price model, corresponding to the expected payoff of the option security.