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Research
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- Financial engineering, optimal control, high-performance computing
- Numerical methods for partial integro-differential equations, arising in option pricing with jump-diffusion and Levy processes
- Stochastic optimal control and Hamilton-Jacobi-Bellman equations, arising in pricing in incomplete markets
- Application of high-performance architectures, such as Cell BE or GPU, to solve aforementioned problems quickly
- A Levy Based Framework for Commodity Derivative Valuation via FFT (with Sebastian Jaimungal) (November 17, 2008) [SSRN] [BIB]
Energy commodities, such as oil, gas and electricity, lack the liquidity of equity markets, have large costs associated with storage, exhibit high volatilities and can have significant spikes in prices. Furthermore, and possibly most importantly, commodities tend to revert to long run equilibrium prices. Many complex commodity contingent claims exist in the markets, such as swing and interruptible options; however, the current method of valuation relies heavily on Monte Carlo simulations and tree based methods. In this article, we develop a new framework for dealing with mean-reverting jump-diffusion (and pure jump) models by working in Fourier space. The method is based on the Fourier space time stepping algorithm of Jackson, Jaimungal, and Surkov (2008), but is tailored for mean-reverting models. We demonstrate the utility of the method by applying it to the valuation of European, American and barrier options on a single underlier, European and Bermudan spread options on two-dimensional underliers, and swing options.
- Stepping Through Fourier Space (with Sebastian Jaimungal) (October 9, 2008) [SSRN]
Diverse finite-difference schemes for solving pricing problems with Levy underliers have been used in the literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated, the methods are difficult to extend to higher dimensions and cannot easily incorporate regime switching or stochastic volatility. We present a new efficient approach which switches between Fourier and real space as time propagates backwards. We dub this method Fourier Space Time-Stepping (FST). The FST method applies to regime switching Levy models and is applicable to a wide class of path-dependent options (such as Bermudan, barrier, shout and catastrophe linked options) and options on multiple assets.
More papers
- FFT-Based Option Pricing under Mean-Reverting Levy Processes (July 19, 2008) [PDF]
Fifth World Congress of Bachelier Finance Society at Imperial College of London
- Parallel Option Pricing with Fourier Space Time-stepping Method on Graphics Processing Units (April 18, 2008) [PDF]
The First Workshop on Parallel and Distributed Computing in Finance at University of Toronto
More presentations
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FST is a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The FST framework circumvents the problems associated with the existing finite difference methods by utilizing the Fourier transform to solve the PIDE, with resulting method being highly efficient and rapidly convergent. FST-based algorithms can can be applied to pricing of a wide range of options such as European, Bermudan, American, barrier, and other options. The dynamics of the stock price process can be modeled by any exponential Levy model, such as Black-Scholes-Merton, Merton jump-diffsuion, Kou jump-diffusion, Variance Gamma, Normal inverse Gaussian and CGMY models, with mean-reversion or regime-switching being easily handled.
More on FST framework or try the online option calculator
- The raytracer was written from scratch in C++ for an undergraduate project in graphics. Some of the features implemented include: anti-aliasing, reflections, refractions, bounding volume hierarchies, bitmap and mathematical textures.
More on raytracer
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