Spectral methods for volatility derivatives

Abstract: 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 created 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 use a regime switching model with jumps and local volatility defined in [1] and calibrate it to the European options on the S&P 500 for a broad range of strikes and maturities. The main idea of this paper is to “lift” (i.e. extend) the generator of the underlying process to keep track of the relevant path information, namely the realized variance. The lifted generator is too large a matrix to be diagonalized numerically. We overcome this difficulty by applying a new semi-analytic algorithm for block-diagonalization. This method enables us to evaluate numerically the

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Postprint ; begutachtet (peer reviewed) ; In: Quantitative Finance ; 9 (2009) 6 ; 663-692

Classification and Topics

• Classification: Wirtschaft

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Mannheim
• (when): 2009
• Creator: Mijatovic, Aleksandar ; Albanese, Claudio ; Lo, Harry

Further information

• DOI: 10.1080/14697680902773603
• URN: urn:nbn:de:0168-ssoar-221488
• Rights: Open Access unbekannt; Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:45 PM CET