Pricing and Hedging Asian-Style Options in Energy

35 Pages Posted: 25 Sep 2013 Last revised: 27 Sep 2014

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Nils Detering

University of California, Santa Barbara (UCSB)

Date Written: August 14, 2014

Abstract

We solve the problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted. Liquid trading in the future is only possible up to the start of a so-called delivery period. After the start of the delivery period, the hedge positions can not be adjusted anymore until maturity. This reflects the trading situation at the Nordic energy market Nord Pool for example. We show that there exists a unique solution to this combined continuous-discrete quadratic hedging problem if the future price process is a special semimartingale with bounded mean-variance tradeoff. Additionally, under the assumption that the future price process is a local martingale, the hedge positions before the averaging period are inherited from the market specification without trading restriction. As an application we consider three models and derive their quadratic hedge positions in explicit form, a simple Black Scholes model with time-dependent volatility, the stochastic volatility model of Barndorff-Nielsen and Shephard and an exponential additive model. Based on an exponential spot price model driven by two NIG \levy processes, we determine an exponential additive model for the future price by moment matching techniques. We calculate hedge positions and determine the quadratic hedge error in a simulation study.

Keywords: Asian options, energy markets, trading restrictions, quadratic hedging, moment matching

JEL Classification: C61, G11, G12, G13

Suggested Citation

Benth, Fred Espen and Detering, Nils, Pricing and Hedging Asian-Style Options in Energy (August 14, 2014). Available at SSRN: https://ssrn.com/abstract=2330273 or http://dx.doi.org/10.2139/ssrn.2330273

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Nils Detering (Contact Author)

University of California, Santa Barbara (UCSB) ( email )

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