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Journal of Economics and Finance

Erschienen in:

01.01.2013

Crack spread option pricing with copulas

verfasst von: Hemantha S. B. Herath, Pranesh Kumar, Amin H. Amershi

Erschienen in: Journal of Economics and Finance | Ausgabe 1/2013

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Abstract

A copula-based approach for pricing crack spread options is described. Crack spread options are currently priced assuming joint normal distributions of returns and linear dependence. Statistical evidence indicates that these assumptions are at odds with the empirical data. Furthermore, the unique features of energy commodities, such as mean reversion and seasonality, are ignored in standard models. We develop two copula-based crack spread option models using a simulation approach that address these gaps. Our results indicate that the Gumbel copula and standard models (binomial, and Kirk and Aron (1995)) mis-price a crack spread option and that the Clayton model is more appropriate. We contribute to the energy derivatives literature by illustrating the application of copula models to the pricing of a heating oil–crude oil “crack” spread option.

Vorheriger Artikel Informational externalities of initial public offerings: Does venture capital backing matter?

Nächster Artikel The productivity and performance of Australia’s major banks since deregulation

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Throughout the article we use the generic term “crack spread option” although the model specifically refers to a heating oil–crude oil crack spread option (NYMEX trading symbol CH). The copula approach is similar for pricing a gasoline oil–crude oil “crack” spread option (NYMEX trading symbol CG).

We would like to acknowledge Bob Biolsi of the CME Group for providing us with insight into how the settlement prices are determined.

More generally, the marginal distributions and joint distribution of the random variables must be elliptical distributions (such as multivariate normal, multivariate t-distribution, logistic distribution, and Laplace distributions).

We wish to sincerely thank the anonymous referees for suggesting the Laurence and Wang (2009) article which has helped improve an earlier version of this article considerably.

In the daily NYMEX crude oil and heating oil futures price data (519 parallel observations) over the period February 3, 2003, to March 3, 2005, we find no evidence of seasonality for both price series. The chi-square test statistic values are 6.84 (p-value = 0.81) for crude oil and 14.52 (p-value = 0.21) for heating oil respectively.

Dornier and Queruel (2000) include an additional term in order to consider seasonality in a mean-reverting model.

While we only need the payoff at maturity to price the European-type crack spread option discussed in this paper, we generate the full random paths for the assets as an illustration since the copula simulation technique can be used for pricing other path dependent options (e.g., American type) in the energy sector.

The options data include the following items: “symbol,” “trading date,” “contract month,” “open interest,” “Call (c)/Put (p),” “strike price,” “High,” “Low,” “Last,” “Settlement Price (Actual Price),” and “Total Volume.”

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Titel: Crack spread option pricing with copulas
verfasst von: Hemantha S. B. Herath
Pranesh Kumar
Amin H. Amershi
Publikationsdatum: 01.01.2013
Verlag: Springer US
Erschienen in: Journal of Economics and Finance / Ausgabe 1/2013
Print ISSN: 1055-0925
Elektronische ISSN: 1938-9744
DOI: https://doi.org/10.1007/s12197-011-9171-1

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