Currency Option Valuation
Option valuation involves the mathematics of stochastic processes. The term stochastic means random, and stochastic processes model randomness. Since its introduction in the 1970s, study of stochastic processes has revolutionized asset valuation. Although the mathematics of stochastic processes can be intimidating, the good news is that it doesn't take a rocket scientist to use options to hedge financial price risks, such as currency risk, using the option payoff profiles in the body of this chapter. The option pricing models in this appendix will help those with an interest in options to develop a deeper understanding of how option prices move with changes in the option value determinants.
The Black-Scholes option pricing model
In 1973, Fischer Black and Myron Scholes borrowed a model from fluid dynamics to solve for the value of a European option on a non-dividend-paying stock. Their Black-Scholes option pricing model triggered a worldwide boom in options trading on financial assets, including currencies.
The key assumption in the Black-Scholes model is that continuously compounded returns on the share price underlying the option are normally distributed with constant mean and standard deviation σ. Instantaneous return on the underlying stock is , where μ and σ are the instantaneous mean and standard deviation of return, dt is an instant ...