A note on commodity contingent valuation
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Garcı´a is completing his PhD in Mathematics and Economics at the University of Oviedo (Spain). He holds a Master’s degree in Economics and Finance from CEMFI (Madrid, Spain) and a degree in Mathematics from the University of Oviedo. Javier Poblacio´n is an economist at the Banco de Espan˜a (Spanish Central Bank); he works in the risk model group. He is completing his PhD in Economics and Finance at the University of Alicante (Spain) and holds a Master’s degree in Economics and Finance from CEMFI (Madrid, Spain) in addition to a degree in Physics from the Complutense University of Madrid. He previously worked for the Spanish oil company Repsol YPF in the risk-management department. Gregorio Serna is an associate professor of Financial Economics at the University of Castilla-La Mancha, Toledo (Spain). He holds a PhD in Economics from the University Carlos III of Madrid (Spain). He has published research papers in the Journal of Banking and Finance, European Financial Management and The Quarterly Review of Economics and Finance, among others.
Practical applications Commodity contingent valuation typically involves complex procedures, like limit steps, partial differential equations or approximations. These ad hoc solutions can only be used in the concrete problem for which they are developed. This paper tries to review and clarify stochastic calculus in the commodity contingent valuation context, simplifying formulae and deductions. This approach allows for a relatively simple pricing of all sorts of financial derivatives on commodity prices, avoiding limit steps, partial differential equations and approximations. Moreover, it has been shown how to obtain precise estimators of prices for NYMEX WTI crude oil futures contracts, in a two-factor context. Abstract
Journal of Derivatives & Hedge Funds, Vol. 13 No. 4, 2008, pp. 311–320 r 2008 Palgrave Macmillan Ltd 1753-9641 $30.00
Given the complex dynamics of commodity prices, most of the papers on the valuation of commodity contingent claims present ad hoc solutions, which are very complex and sometimes include approximations. This paper shows how well-known techniques and results in stochastic calculus can be used to simplify formulae and deductions. Specifically, we show how to obtain more precise estimators of the parameters in the two-factor model by Schwartz than the approximations given by
the author, which tend to overestimate the parameters. These divergences are important in the valuation of commodity contingent claims. Journal of Derivatives & Hedge Funds (2008) 13, 311–320. doi:10.1057/palgrave.jdhf.1850079
Keywords: stochastic calculus; commodity prices; mean–reverting processes; two-factor models; volatility
Journal of Derivatives & Hedge Funds Volume 13 Number 4 2008 www.palgrave-journals.com/jdhf
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INTRODUCTION Since the now classical Black and Scholes1 paper, Itoˆ calculus has become a dominant approach in dealing with financial markets. Following this approach, there have been many papers assuming that commodity prices follow a geometric Brownia
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