Pricing derivatives written on more than one underlying asset in a multivariate Lévy framework
Grégory Rayée (ULB, Belgium)
Joint work with Grisleda Deelstra and Laura Ballotta

Thursday June 5, 16:30-17:00 | session 9.6 | Calibration | room L

In this paper, we study the pricing of products written on several assets with a multivariate exponential Lévy model. Using the Esscher transform for multidimensional semimartingales, we relate Exchange and Quanto options to European call and Put options. We derive an FFT based pricing formula for Exchange and Quanto options. We present a fast calibration method to the Vanilla market and to the Exchange and Quanto market. We illustrate this method in a subordinated Brownian motion framework with as particular examples the Variance Gamma and the Normal Inverse Gaussian models.

Calibration of local correlation models to basket smiles
Julien Guyon (Bloomberg L.P., USA)

Thursday June 5, 17:00-17:30 | session 9.6 | Calibration | room L

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the delta. When options on a basket, be it a stock index, a cross FX rate, or an interest rate spread, are liquidly traded, one may want to calibrate a local correlation to these option prices. Only two particular solutions have been suggested so far in the literature. Both solutions impose a particular dependency of the correlation matrix on the asset values that one has no reason to undergo.
By combining the particle method presented in [Being Particular About Calibration, Guyon and Henry-Labordere, 2012] with a new simple idea, we build whole families of calibrated local correlation models, which include the two existing models as special cases. For the first time, one can now design a calibrated local correlation in order to fit a view on the correlation skew, or reproduce historical correlation, or match some exotic option prices, thus improving the pricing, hedging, and risk-management of multi-asset derivatives. We also show how to generalize this technique to calibrate (i) models that combine stochastic interest rates, stochastic dividend yield, local stochastic volatility, and local correlation; and (ii) single-asset path-dependent volatility models.
Numerical results show the wide variety of calibrated local correlations and give insight on a difficult (still unsolved) problem: find lower bounds/upper bounds on general multi-asset option prices given the whole surfaces of implied volatilities of a basket and its constituents.
This research will be published in the February 2014 issue of Risk Magazine. It is available online at http://dx.doi.org/10.2139/ssrn.2283419

Calibration of Stochastic Volatility Models: A Tikhonov Regularization Approach
Min Dai (NUS, Singapore)
Joint work with Xinye Yue and Ling Tang

Thursday June 5, 17:30-18:00 | session 9.6 | Calibration | room L

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach and an efficient numerical algorithm to recover the stochastic volatility model. In contrast to most existing literature, we do not assume that the model has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach.