Option Pricing: Mean Reversion and Multi-Scale Stochastic Volatility

 

Host Institution:

La Trobe University

Title of Seminar:

Option Pricing: Mean Reversion and Multi-Scale Stochastic Volatility

Speaker's Name:

Dr Jing Zhao

Speaker's Institution:

La Trobe University

Time and Date:

Friday 19 November 2010 at 11:00 am

Seminar Abstract:

 

This work investigates the valuation of currency options when the underlying currency follows a mean-reverting lognormal process with multi-scale stochastic volatility. A closed-form solution is derived for the characteristic function of the log-asset price.

European options are then valued by means of the Fourier inversion formula. The proposed model enables us to calibrate simultaneously to the observed currency futures and the implied volatility surface of the currency options within a unified framework.

The fractional fast Fourier transform (FFT) is adopted to implement the Fourier inversion, thus ensuring that the grid spacing restriction of the standard FFT can be relaxed, which results in a more efficient computation. Using Monte Carlo simulation as a benchmark, our numerical examples show that the derived option pricing formula is accurate and efficient for practical use.

 

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