Foucault Pendulum in the Panthéon in Paris
MMF2021 Numerical Methods for Finance Workshop
 
This workshop aims to build on the material taught in MMF2021 and will cover some of the latest numerical methods for options pricing. We develop numerical methods in Matlab for pricing of European, American and barrier options under Black-Scholes-Merton, Merton jump-diffusion and Kou jump-diffusion models. The emphasis will be on actual implementation of the methods with applications to fitting volatility smiles/surfaces and parameter estimation.

Workshop Syllabus

  • Session 1, September 19, 2008 - Convolution quadrature method and implied volatility skew
  • Session 2, September 25, 2008 - Fourier product quadrature and Carr Madan FFT methods, Merton jump-diffusion model
  • Session 3, October 9, 2008 - Implied volatility surface and parameter fitting
  • Session 4, October 23, 2008 - Fourier Space Time-stepping method
  • Session 5, October 30, 2008 - Fourier Space Time-stepping method

Code :

Pricing European options under Black-Scholes-Merton model
CarrMadanFFT_European_BlackScholesMerton.m
ClosedForm_European_BlackScholesMerton.m
FourierProductQuadrature_European_BlackScholesMerton.m
ConvolutionQuadrature_European_BlackScholesMerton.m
FST_European_BlackScholesMerton.m
Driver_European_BlackScholesMerton.m

Pricing European options under Merton jump-diffusion model
CarrMadanFFT_European_MertonJumpDiffusion.m
ClosedForm_European_MertonJumpDiffusion.m
FourierProductQuadrature_European_MertonJumpDiffusion.m
FST_European_MertonJumpDiffusion.m
Driver_European_MertonJumpDiffusion.m

Computing implied volatility surface
ImpliedVolatility.m
SPY_Option_Prices.mat
Driver_ImpliedVolatility.m

Fitting market data
Driver_ParameterFitting_BlackScholesMerton.m
Driver_ParameterFitting_MertonJumpDiffusion.m