Albanese, Claudio and Mijatovic, Aleksandar (2006): SPECTRAL METHODS FOR VOLATILITY DERIVATIVES.

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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 opened the challenge of developing a pricing framework that can simultaneously handle European options, forwardstarts, 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 semianalytic algorithm for blockdiagonalization. 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 forwardstarts and VIX options.
Item Type:  MPRA Paper 

Institution:  Independent Consultant 
Original Title:  SPECTRAL METHODS FOR VOLATILITY DERIVATIVES 
Language:  English 
Keywords:  Volatility derivatives; operator methods 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  5244 
Depositing User:  Claudio Albanese 
Date Deposited:  10 Oct 2007 
Last Modified:  02 Oct 2019 22:48 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/5244 