Monte Carlo

Abstract

Equity derivatives contracts can be valued using closed form solutions, finite difference methods and Monte Carlo simulation. The former two approaches are limited to specific products and models. Closed form solutions are available primarily for European options and affine models as discussed in Chapters 11 and 16. For log-normal assets (approximate) formulae are also known for barrier products, as well as basket and Asian products, see Sections 3.1, 3.3 and 3.8. Finite difference, including tree methods, are important for products with early exercise features, such as American options and convertible bonds. For path-dependent and multi-asset products these methods are of limited use due to the high dimensionality of the state space.