Programme

DAY TWO - Wednesday 9 June 2010

08:30 Registration and coffee

09:00 Fast numerical solutions for jump diffusion models: the standard fast Fourier transform approach

• Fast Fourier transform approach
  • Fast Fourier transform vs discrete Fourier transform: computational costs
  • Danielson-Lanczos representation
  • Cooley-Tuckey algorithm
  • Implementation

10:30 Morning break

11:00 Fast numerical solutions for jump diffusion models: the fractional and non uniform discrete Fourier transforms

• The generalised discrete Fourier transform
  • Generalised convergence theorems for DFT
  • The fractional fast Fourier transform algorithm
  • The non uniform fast Fourier transform algorithm
  • Excel and MATLAB implementation

12:30 Lunch

13:30 Calibration to market data of jump diffusion models: the theory

• The calibration problem
  • An ill-posed problem: dimensions, local minima and operative solutions
  • Local optimizers vs global algorithms
  • The optimal choice of the starting point
  • The optimal choice of the fit measure

15:00 Afternoon break

15:30 Calibration to market data of jump diffusion models: the practice

• Some MATLAB examples of real time calibration of jump diffusion models
  • Stability assessment: resilience of the calibrated parameters to price shocks
  • Error control: analysis of the fitting quality
• Calibrating jump diffusion models on illiquid markets data: operative solutions

17:00 Close of course