×

Model uncertainty in commodity markets. (English) Zbl 1330.91179

Summary: Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-revert to the seasonal trend. Here we model ambiguity by allowing the agent to consider a class of models absolutely continuous w.r.t. their reference model, but penalize candidate models that are far from it. We show that the buyer (seller) of a forward contract introduces a negative (positive) drift in the dynamics of the spot price and enhances downward (upward) jumps so the prices they are willing to trade at are lower (higher) than that of the forward price under \({\mathbb{P}}\). When ambiguity averse buyers and sellers employ the same reference measure they cannot trade because the seller requires more than what the buyer is willing to pay. Finally, we observe that when ambiguity averse agents price options written on the commodity forward, the effect of ambiguity aversion is strongest when the option is at-the-money and weaker when it is deep in-the-money or deep out-of-the-money.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
49J20 Existence theories for optimal control problems involving partial differential equations
Full Text: DOI

References:

[1] K. Bannor, R. Kiesel, A. Nazarova, and M. A. Scherer (2013), {\it Model Risk and Power Plant Valuation}, working paper.
[2] F. Benth and J. Saltyte-Benth (2006), {\it Analytical approximation for the price dynamics of spark spread options}, Stud. Nonlinear Dyn. Econom., 10 pp. 1355-1355. · Zbl 1260.91256
[3] F. E. Benth, R. Biegler-König, and R. Kiesel, {\it An empirical study of the information premium on electricity markets}, Energy Econom., 36 (2013), pp. 55-77.
[4] F. E. Benth, L. Ekeland, R. Hauge, and B. F. Nielsen, {\it A note on arbitrage-free pricing of forward contracts in energy markets}, Appl. Math. Finance, 10 (2003), pp. 325-336. · Zbl 1101.91323
[5] F. E. Benth, J. Kallsen, and T. Meyer-Brandis, {\it A non-Gaussian Ornstein-Uhlenbeck process for electrcity spot price modelling and derivatives pricing}, Appl. Math. Finance, 14 (2007), pp. 153-169. · Zbl 1160.91337
[6] F. E. Benth, J. Saltyte-Benth, and S. Koekebakker, {\it Stochastic Modeling of Electricity and Related Markets}. World Scientific, River Edge, NJ. · Zbl 1143.91002
[7] R. Carmona and M. Coulon, {\it A survey of commodity markets and structural models for electricity prices}, in Quantitative Energy Finance, F. E. Benth, V. A. Kholodnyi, and P. Laurence, eds., Springer, New York, pp. 41-83.
[8] R. Carmona, M. Coulon, and D. Schwarz, {\it Electricity price modeling and asset valuation: A multi-fuel structural approach}, Math. Financ. Econ., 7 (2013), pp. 167-202. · Zbl 1269.91037
[9] Á. Cartea and M. Figueroa, {\it Pricing in electricity markets: A mean reverting jump diffusion model with seasonality}, Appl. Math. Finance, 12 (2005), pp. 313-335. · Zbl 1134.91526
[10] Á. Cartea and S. Jaimungal (2011), {\it Irreversible Investments and Ambiguity Aversion}, SSRN abstract 1961786. · Zbl 1415.91305
[11] Á. Cartea, S. Jaimungal, and R. Donnelly, {\it Algorithmic Trading with Model Uncertainty}, SSRN abstract 2310645. (2014). · Zbl 1407.91287
[12] Á. Cartea and P. Villaplana, {\it Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity}, J. Banking Finance, 32 (2008), pp. 2502-2519.
[13] Á. Cartea and T. Williams, {\it UK gas markets: The market price of risk and applications to multiple interruptible supply contracts}, Energy Economics, 30 (2008), pp. 829-846.
[14] I. Figuerola-Ferretti and J. Gonzalo, {\it Modelling and measuring price discovery in commodity markets}, J. Econometrics, 158 (2010), pp. 95-107. · Zbl 1431.62611
[15] J.-P. Fouque, S. Jaimungal, and M. J. Lorig, {\it Spectral decomposition of option prices in fast mean-reverting stochastic volatility models}, SIAM J. Financial Math., 2 (2011), pp. 665-691. · Zbl 1255.91127
[16] R. Gibson and E. Schwartz, {\it Stochastic convenience yield and the pricing of oil contingent claims}, J. Finance, 45 (1990), pp. 959-976.
[17] M. Guidolin and F. Rinaldi, {\it Ambiguity in asset pricing and portfolio choice: A review of the literature}, Theory Decision, 74 (2013), pp. 183-217. · Zbl 1268.91164
[18] B. Hambly, S. Howison, and T. Kluge, {\it Modelling spikes and pricing swing options in electricity markets}, Quant. Finance, 9 (2009), pp. 937-949. · Zbl 1182.91176
[19] L. Hansen and T. Sargent, {\it Robust control and model uncertainty}, Amer. Econom. Rev., 91 (2001), pp. 60-66.
[20] L. P. Hansen and T. J. Sargent, (2007) {\it Robustness}, Princeton University Press, Princeton, NJ.
[21] S. Hikspoors and S. Jaimungal, {\it Energy spot price models and spread options pricing}, Int. J. Theoret. Appl. Finance, 10 (2007), pp. 1111-1135. · Zbl 1153.91422
[22] S. Hikspoors and S. Jaimungal, {\it Asymptotic pricing of commodity derivatives for stochastic volatility spot models}, Appl. Math. Finance, 15 (2008), pp. 449-447. · Zbl 1156.91374
[23] S. Jaimungal and G. Sigloch, {\it Incorporating risk and ambiguity aversion into a hybrid model of default}, Math. Finance, 22 (2012), pp. 57-81. · Zbl 1278.91176
[24] S. Jaimungal and V. Surkov, {\it Lévy-based cross-commodity models and derivative valuation}, SIAM J. Financial Math., 2 (2011), pp. 464-487. · Zbl 1236.91143
[25] A. Roncoroni (2002), {\it A Class of Marked Point Processes for Modeling Electricity Prices}, Ph.D. dissertation, Université Paris IX Dauphine.
[26] E. Schwartz, {\it The stochastic behavior of commodity prices: Implications for valuation and hedging}, J. Finance, 52 (1997), pp. 923-973.
[27] E. S. Schwartz and J. Smith, {\it Short-term variations and long-term dynamics in commodity prices}, Management Sci., 46 (2000), pp. 893-911.
[28] G. Stahl, J. Zheng, R. Kiesel, and R. Rühlicke (2012), {\it Conceptualizing robustness in risk management}, SSRN 2065723.
[29] A. B. Trolle and E. S. Schwartz (2009), {\it Unspanned stochastic volatility and the pricing of commodity derivatives}, Rev. Financial Stud., 22, pp. 4423-4461.
[30] R. Uppal and T. Wang, {\it Model misspecification and under diversification}, J. Finance, 58 (2003), pp. 2465-2486.
[31] R. Weron (2007), {\it Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach}, Wiley, New York.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.