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# Interest Rate Modelling: Pricing Options via Fourier Inversion & Simulation of Stochastic Volatility Models

**Pricing Options via Fourier Inversion & Simulation of Stochastic Volatility Models**

Presenter: Roger Lord: Head of Quantitative Analytics, Cardano

Presenter: Roger Lord: Head of Quantitative Analytics, Cardano

**Course Running Time: 6 Hours**

**Session 1: (Running Time: 01:15:54)**

**Session 2**** (Running Time: 1:37:34)**

**Session 3****: (Running Time: 46:16)**

**Session 4**** (Running Time: 1:01:35)**

**Session 5: (Running Time: 1:20:28)**

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