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Pricing Options via Fourier Inversion & Simulation of Stochastic Volatility Models

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Pricing Options via Fourier Inversion & Simulation of Stochastic Volatility Models

Presenter: Roger Lord: Head of Quantitative Analytics, Cardano 

Within this workshop we will explore two topics that are important to the modern day pricing of derivatives - the Monte Carlo simulation of stochastic volatility models, as well as how to price options by using Fourier inversion techniques.

The first part of the workshop will focus on techniques to efficiently simulate stochastic volatility models such as Heston, Schöbel-Zhu and SABR. Pitfalls of using too simple methods are shown, and lessons are learned from more sophisticated methods that are applicable in a wide variety of stochastic volatility models.

The second part will be focussed on the usage of Fourier inversion techniques to price options. Since the characteristic function of many, typically affine, models can be expressed in closed-form, one can price vanilla options by means of Fourier inversion. We will show how to derive the characteristic function of such models, and focus on how to compute these efficiently by means of choosing an optimal contour, or via control variates.

  • An overview of stochastic volatility models (e.g. Heston, Schöbel-Zhu, SABR)
  • Pitfalls using Euler or higher-order schemes
  • Leaking correlation
  • Moment-matching schemes
  • Derivation of characteristic function in affine models
  • Option pricing using Fourier inversion
  • Caveats using complex logarithms
  • Choosing the optimal dampening coefficient
  • Usage of control variates



Monte Carlo

Published date

14 March 2014



Presenter Bio

Roger Lord

Roger currently heads up the quantitative analytics group at Cardano, focussing on the pricing of derivatives across asset classes, as well as their inclusion in risk management strategies for institutional investors. In addition he also lectures in interest rate derivative pricing at the Duisenberg School of Finance, and the University of Amsterdam. Previously he was a front-office exotics quant for the exotic interest rate derivatives business at Rabobank International in London, and a model validator at the same bank. Roger has written his PhD thesis at Erasmus University Rotterdam on the efficient pricing algorithms for exotic derivatives, and holds an MSc in Applied Mathematics and Econometrics. He has published several papers on option pricing using Fourier techniques as well as simulation methods for stochastic volatility models.

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