American CatEPut Price Surface
American Spread Option Exercise Surface
Results of MSc Thesis
 
Research
Current research interests:
  • Mathematical finance and stochastic calculus
  • 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
Papers:
  • Parallel Option Pricing with Fourier Space Time-stepping Method on Graphics Processing Units  (October 8, 2007) [SSRN]
    With the evolution of Graphics Processing Units (GPUs) into powerful and cost-efficient computing architectures, their range of application has expanded tremendously, especially in the area of computational finance. Current research in the area, however, is limited in terms of options priced and complexity of stock price models. This paper presents algorithms, based on the Fourier Space Time-stepping (FST) method, for pricing single and multi-asset European and American options with Levy underliers on a GPU. Furthermore, the single-asset pricing algorithm is parallelized to attain greater efficiency.

  • Option Pricing with Regime Switching Levy Processes Using Fourier Space Time-stepping (with Ken Jackson and Sebastian Jaimungal)  (April 30, 2007) [PDF] [BIB]
    Although jump-diffusion and Levy models have been widely used in industry, the pricing partial-integro differential equations poses various difficulties for valuation. Diverse finite-difference schemes for solving the problem have been introduced in the literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated and the methods are difficult to extend to higher dimensions. We present a new efficient transform approach for regime-switching Levy models which is applicable to a wide class of path-dependent options (such as Bermudan, barrier, and shout options) and options on multiple assets.

  • Fourier Space Time-stepping for Option Pricing with Levy Models (with Ken Jackson and Sebastian Jaimungal)  (March 14, 2007) [SSRN]
    It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro differential equation (PIDE) and although several approaches for solving the PIDE have been suggested in the literature, none are entirely satisfactory. All treat the integral and diffusive terms asymmetrically and are difficult to extend to higher dimensions. We present a new, efficient algorithm, based on transform methods, which symmetrically treats the diffusive and integrals terms, is applicable to a wide class of path-dependent options (such as Bermudan, barrier, and shout options) and options on multiple assets, and naturally extends to regime-switching Levy models. We present a concise study of the precision and convergence properties of our algorithm for several classes of options and Levy models and demonstrate that the algorithm is second-order in space and first-order in time for path-dependent options.

  • Valuation of Mortgage-Backed Securities in a Distributed Environment (February 18, 2004) [PDF]
    Valuation of Mortgage-Backed Securities, regarded as integration in high-dimensional space, can be readily performed using the Monte Carlo method. The Quasi-Monte Carlo method, by utilizing low-discrepancy sequences, has been able to achieve better convergence rates at computational finance problems despite analysis suggesting that the improved convergence comes into effect only at sample sizes growing exponentially with dimension. This may be attributed to the fact that the integrands are of low effective dimension and quasi-random sequences' good equidistribution properties in low dimensions allow for the faster convergence rates to be attained at feasible sample sizes. The Brownian bridge discretization is traditionally used to reduce the effective dimension although an alternate choice of discretization can produce superior results. This paper examines the standard Brownian bridge representation and offers a reparametrization to further reduce dimension. The performance is compared both in terms of improvement in convergence and reduced effective dimensionality as computed using ANOVA decomposition. Also, porting of the valuation algorithm to a distributed environment using Microsoft .NET is presented.
Presentations: