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Spectral methods for volatility derivatives


Mijatovic, Aleksandar; Albanese, Claudio; Lo, Harry


Bitte beziehen Sie sich beim Zitieren dieses Dokumentes immer auf folgenden Persistent Identifier (PID):http://nbn-resolving.de/urn:nbn:de:0168-ssoar-221488

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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 joint distribution between the underlying stock price and the realized variance, which in turn gives us a way of pricing consistently European options, general accrued variance payoffs and forward-starting and VIX options.
Klassifikation Volkswirtschaftslehre; Wirtschaftsstatistik, Ökonometrie, Wirtschaftsinformatik
Freie Schlagwörter Volatility modelling; Volatility smile fitting; Volatility surfaces; Stochastic volatility Quantitative finance
Sprache Dokument Englisch
Publikationsjahr 2009
Seitenangabe S. 663-692
Zeitschriftentitel Quantitative Finance, 9 (2009) 6
DOI http://dx.doi.org/10.1080/14697680902773603
Status Postprint; begutachtet (peer reviewed)
Lizenz PEER Licence Agreement (applicable only to documents from PEER project)