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Spectral methods for volatility derivatives
[journal article]
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 ... view more
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.... view less
Classification
Economic Statistics, Econometrics, Business Informatics
Political Economy
Free Keywords
Volatility modelling; Volatility smile fitting; Volatility surfaces; Stochastic volatility Quantitative finance
Document language
English
Publication Year
2009
Page/Pages
p. 663-692
Journal
Quantitative Finance, 9 (2009) 6
DOI
https://doi.org/10.1080/14697680902773603
Status
Postprint; peer reviewed
Licence
PEER Licence Agreement (applicable only to documents from PEER project)