Pricing Financial Derivatives in the Hull–White Model Using Cubature Methods on Wiener Space

This chapter discusses the idea of cubature formulae on Wiener space. It briefly explains the theory behind the idea of the cubature method and compares and contrasts it with the classical Monte Carlo simulation. The chapter reviews how the cubature formulae of degree 5 can be used in security market models, namely in the Samuelson price process to estimate the price of European call and put options. It also reviews the idea of constructing a recombining trinomial tree in the Black–Scholes model to price path‐dependent derivatives. The chapter focuses on the interest‐rate models and explores the Hull–White one‐factor model to study the application of the cubature formula in the fixed‐income market models. In order to price financial derivatives via cubature method, more possible random values are needed to be accessed each time. Iteration of the cubature formula which results in obtaining a non‐recombining trinomial tree is performed.