you are all invited to participate in the following seminar organized by QFinLab – Department of Mathematics, Politecnico di Milano.

 

Seminar room, third floor, building 14, Via Bonardi 9, Milano (Leonardo Campus); online (Microsoft Teams), Link

 

Riccardo Brignone (University of Pavia)

 

Title: Pricing path-dependent options under stochastic volatility models with arbitrary accuracy

Abstract: We propose a unified methodology for pricing general path-dependent derivatives, such as (without sake of exhaustiveness) Asian, barrier, variance, lookback and cliquet options. The proposed approach is based on the Monte Carlo Conditional Fourier-cosine method and works for a broad class of stochastic volatility models. The main benefit of the new algorithm over existing literature consists in a simple and effective control of the error. A practitioner needs to provide the pricing algorithm with two parameters: i) a probability, q; ii) an error tolerance,  epsilon. Then, our proposed algorithm provides a price approximation that differs by no more than epsilon from the true unknown option price with probability at least equal to q. In other words, the practitioner can easily control the accuracy of the price approximation, contrarily to any other approach proposed in the literature so far. We provide explicit formulas linking the variance of the Monte Carlo simulation estimator of the option price, the error tolerance, and the number of simulations. Leveraging such formulas, it is possible to drastically reduce computing times through variance reduction techniques, rendering the pricing methodology computationally efficient.

 

 

The organizers: Michele Azzone and Alessandro Calvia