Pricing stochastic volatility models using random grids

Rajkumar, Rishay

Pricing stochastic volatility models using random grids

Master Thesis

2022

Abstract

Assets can be priced using a variety of numerical methods. In some instances, a particular numerical method may be more appropriate than others. If one method is used to calibrate the model to market conditions, but another method is used to price the asset, the results obtained may be inconsistent. This dissertation addresses the fundamental problem of this bias that is introduced when calibrating and pricing options using inconsistent methods. The random grids approach, developed by Andreasen and Huge (2011), is a pricing method that guarantees discrete consistency between calibration, finite difference solution and Markov-chain MonteCarlo simulation based on the random grids approach. This dissertation provides a review and implementation of this random grids approach for pricing under the Heston model as well as the stochastic local volatility model. Consistent results are obtained for a call option under the various pricing methods using similar parameters as those used in the random grids paper. More specifically, when using a Heston model, consistent prices are obtained for the characteristic function pricing method, the backward finite difference method, the forward finite difference method as well as the Markov-chain Monte-Carlo method based on the random grids approach. Similarly, consistent prices are obtained under the stochastic local volatility model for the backward finite difference method, the forward finite difference method and the Markov-chain Monte-Carlo method based on the random grids approach.

Keywords

finance and tax

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