Efficient Monte Carlo Pricing in the Heston Model: A Composite Integration Approach

Specialeforsvar ved Nicolai Henriksen

Titel: Efficient Monte Carlo Pricing in the Heston Model: A Composite Integration Approach

Abstract: The Heston model is arguable one of the more popular stochastic volatility models, since it allows for semi-analytic closed-form expression for simple contingent claims such as the European Call option. The pricing of complex or path dependent options relies on the other hand on standard numerical procedures, where the Monte Carlo method often is the last resort.
The Heston model has exists for over twenty six years, however the creation of an efficient Monte Carlo method seems only to have interested a few. The efficiency of the existing methods are furthermore frequently reported to be determined solely by the simulation scheme, thus the underlying features, such as the random number generator and the transformation algorithms are often taken for granted.
The goal of this thesis is therefore to present an efficient Monte Carlo method for the pricing in Heston’s model, which in particular implies, that the Monte Carlo method most be easily parallelizable. The Monte Carlo method presented here introduces a new collection of simulation schemes, namely the Quadratic Exponential Composite Integration schemes, which exhibits a promising speed-accuracy trade-off compared with existing schemes. Numerical tests suggests in particular, that the schemes are favourable compared to existing schemes for little to moderate path dependent options.

Vejleder: Rolf Poulsen
Censor:   David Sloth Pedersen, Danske Bank