ABSTRACT
This chapter discusses option pricing methods mainly within the original Black/Scholes framework, which for a large range of applications still remains the dominant paradigm. The key assumption of the Black/Scholes model is that the underlying asset(s) exhibit deterministic proportional volatility. Whenever this assumption holds, Black/Scholes-type derivative pricing formulae follow. The chapter also covers a selection of exotic options with closed form pricing formulae in the Black/Scholes framework. An option to exchange one asset for another would commonly be considered an “exotic” option, as opposed to the standard “plain vanilla” European calls and puts. The chapter illustrates how standard options are special cases of a more general, “exotic” payoff structure. For discretely monitored barrier and lookback options, the exercise dimension increases with the number of monitoring dates, quickly compounding the computational effort required to price the option.
