Sequential Calibration of Asset Pricing Models to Option Prices

Oagile, Joel

Sequential Calibration of Asset Pricing Models to Option Prices

Master Thesis

2018

Publisher

University of Cape Town

Department

African Institute of Financial Markets and Risk Management

Faculty

Faculty of Commerce

Abstract

This paper implements four calibration methods on stochastic volatility models. We estimate the latent state and parameters of the models using three non-linear filtering methods, namely the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF) and the unscented Kalman filter (UKF). A simulation study is performed and the non-linear filtering methods are compared to the standard least square method (LSQ). The results show that both methods are capable of tracking the hidden state and time varying parameters with varying success. The non-linear filtering methods are faster and generally perform better on validation. To test the stability of the parameters, we carry out a delta hedging study. This exercise is not only of interest to academics, but also to traders who have to hedge their positions. Our results do not show any significant benefits resulting from performing delta hedging using parameter estimates obtained from non-linear filtering methods as compared to least square parameter estimates.

Keywords

Mathematical Finance

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