Spectral Methods For Volatility Derivatives
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This opened the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and options on the VIX. In this paper we propose a new approach to this problem using spectral methods. We define a stochastic volatility model with jumps and local volatility, which is almost stationary, and calibrate it to the European options on the S&P 500 for a broad range of strikes and maturities. We then extend the model, by lifting the corresponding Markov generator, to keep track of relevant path information, namely the realized variance. The lifted generator is too large a matrix to be diagonalized numerically. We overcome this diculty by developing a new semi-analytic algorithm for block-diagonalization. This method enables us to evaluate numerically the joint distribution between the underlying stock price and the realized variance which in turn gives us a way of pricing consistently the European options, general accrued variance payos as well as forward-starts and VIX options.
|Date of creation:||01 Mar 2006|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
- Claudio Albanese & Aleksandar Mijatović, 2009. "A Stochastic Volatility Model For Risk-Reversals In Foreign Exchange," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 877-899.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Peter Friz & Jim Gatheral, 2005. "Valuation of volatility derivatives as an inverse problem," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 531-542.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:5244. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.