DSAS Colloquium - Javad Rastegari Koopaei

Speaker: Javad Rastegari Koopaei (Western)

Title: Option Pricing with Conditionally Affine GARCH Models

Abstract:

Conditional Hetereskedasticity models (GARCH) are well-known tools for valuation of options and other derivatives in discrete time. For certain types of GARCH models, known as affine GARCH, one can find a semi-closed form for the moment generating function of future asset returns. The moment generating function combined with Fourier techniques leads to pricing formulas for European vanilla options, thus providing a faster method of option pricing compared to pure Monte Carlo simulation.

In this talk, we will introduce a Conditionally GARCH model with an emphasis on the conditional affine structure. We review the affine GARCH model of Heston-Nandi and generalize it to a conditional affine GARCH. The result is a pricing formula which combines the Fourier transform method and Monte Carlo simulation.

As the main example of our conditional affine GARCH, we propose a Markov-switching affine GARCH model (MS-GARCH). We use a Markov chain with two states representing periods of low-volatility and high-volatility in the market.

Finally, We will demonstrate examples of MS-GARCH option prices with comparison to Black-Scholes and Heston-Nandi prices as benchmarks. We will also discuss different methods of implementing the pricing formula and their performance compared to the pure Monte Carlo method.

This is joint work with Dr. Marcos Escobar and Dr. Lars Stentoft.