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Commodities Model
  • Is Multi-Factor Really Necessary to Price European Options in Commodity? The main result of this article is the presentation of the Distribution Match Method. This method applies to a general multi-factor pricing model under assumption of normal law drift. The idea is to find an equivalent one-factor model for European options. The equivalent model admits a weak solution, which has the same one-dimensional marginal probability distribution. Moreover, the one-dimensional distribution can be explicitly calculated under certain condition. This result can consequently induct closed formula for the future price and European option price. We apply these results to two well known commodity models, the Gabillon and the Gibson Schwartz model, to provide the price for the future price and a closed formula for the European options. , E. Benhamou, Z. Wang, A.G. Galli (2009)
  • Markov Models for Commodity Futures: Theory and Practice , L.Andersen (2008)
  • Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives , A.B.Trolle, E.S.Schwartz (2008)
  • A dependence model for pairs of commodity forward curves: application to the US natural gas and oil markets , S.Ohana (2007)
  • Arbitrage free cointegrated models in gas and oil future markets In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions. Under the risk neutral probabil- ity, the motions of both energies are correlated Brownian motions while under the historical probability, they are cointegrated by a Vectorial Error Correction Model. Our approach is equivalent to defining the market price of risk. This model is free of arbitrage: thus, it can be used for risk management as well for option pricing issues. Calibration on European market data and numerical simulations illustrate well its behavior. , G.Benmenzer, E.Gobet, C.Jerusalem (2007)
  • On the Pricing and Hedging of Options on Commodity Forward and Futures Contracts - A Note , V.Zakamouline (2007)
  • Optimal quantization for the pricing of swing options , O.Bardou, S.Bouthamy, G.Pag?s (2007)
  • A Multi-factor Jump-Diffusion Model for Commodities , J. Crosby (2006)
  • Valuing Real Options using Implied Binomial Trees and Commodity Futures Options , T. Arnold, T. Falcon Crack, A. Schwartz (2005)
  • Calibration of the multi-factor HJM model for energy market The purpose of this paper is to show that using the toolkit of interest rate theory, already well known in financial engineering as the HJM model [D. Heath, R. Jarrow, A. Morton, Econometrica 60, 77 (1992)], it is possi ble to derive explicite option pricing formula and calibrate the theoretical model to the empirical electricity market. The analysis is illustrated by numerical cases from the European Energy Exchange (EEX) in Leipzig. The multifactor versus onefactor HJM models are compared. , E. Broszkiewicz-Suwaj, A. Weron (2005)
  • A Numerical Method for Pricing Electricity Derivatives for Jump-Diffusion Processes Based on Continuous Time Lattices , C.Albanese, H.Lo, S.Tompaidis (2005)
  • Stochastic Behavior of Spot and Futures Commodity Prices: Theory and Evidence , J. Casassus (2004)
  • A Two-Factor Model for Commodity Prices and Futures Valuation , D.R.Ribeiro, S.D.Hodges (2004)
  • A bootstrap approach to the price uncertainty of weather derivatives , O. Roustant, J.-P. Laurent, X. Bay, L. Carraro (2003)
  • Spot Convenience Yield Models for Energy Assets , M.Ludkovski, R.Carmona (2003)
  • COMMODITY PRICE MODELING THAT MATCHES CURRENT OBSERVABLES: A NEW APPROACH We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously obtain all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions. , K.R.Miltersen (2002)
  • Pricing Electricity Forwards Under Stochastic Volatility , B.P.Kellerhals (2001)
  • Valuing Energy Options in a One Factor Model Fitted to Forward Prices In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Strickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style and exotic energy derivatives can be priced using trinomial trees, which are constructed to be consistent with the forward curve and volatility structure. We demonstrate the application of the trinomial tree to the pricing of a European and American Asian option. The analysis in this paper extends the results in Schwartz [1997] and Amin, et al. [1995]. , L.Clewlow, C.Strickland (1999)

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