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Calibrating a market model with stochastic volatility to commodity and interest rate risk

Karlsson, Patrik LU ; Pilz, Kay and Schlögl, Erik (2016) In Quantitative Finance
Abstract
Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices.Aprocedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices... (More)
Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices.Aprocedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices (cross-correlation). When calibrating to options on forwards (rather than futures), the fitting of cross-correlation preserves the (separate) calibration in the two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross-correlation is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the ‘orthonormal Procrustes’ problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
calibration, commodity markets, derivative pricing, interest rate modelling, interest rate derivatives, oil futures, energy derivatives
in
Quantitative Finance
pages
19 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85006894317
ISSN
1469-7688
DOI
10.1080/14697688.2016.1254814
language
English
LU publication?
no
id
f9ab1db2-8bcb-4d20-a9fe-471201adc400
date added to LUP
2016-12-27 14:57:26
date last changed
2017-04-02 04:33:53
@article{f9ab1db2-8bcb-4d20-a9fe-471201adc400,
  abstract     = {Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices.Aprocedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices (cross-correlation). When calibrating to options on forwards (rather than futures), the fitting of cross-correlation preserves the (separate) calibration in the two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross-correlation is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the ‘orthonormal Procrustes’ problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures.},
  author       = {Karlsson, Patrik and Pilz, Kay and Schlögl, Erik},
  issn         = {1469-7688},
  keyword      = {calibration,commodity markets,derivative pricing,interest rate modelling,interest rate derivatives,oil futures,energy derivatives},
  language     = {eng},
  month        = {12},
  pages        = {19},
  publisher    = {Taylor & Francis},
  series       = {Quantitative Finance},
  title        = {Calibrating a market model with stochastic volatility to commodity and interest rate risk},
  url          = {http://dx.doi.org/10.1080/14697688.2016.1254814},
  year         = {2016},
}