Avaliação de opções de swing em contratos de gás natural usando um modelo de dois fatores
Pricing swing options embedded in natural gas contracts using a two-factor model
Samanez, Carlos Patricio; Costa, Leticia de Almeida
http://dx.doi.org/10.1590/S0103-65132013005000084
Production, vol.24, n4, p.760-775, 2014
Resumo
No mercado de gás natural (GN), muitos contratos incorporam flexibilidades no volume, conhecidas como opções de swing, as quais concedem ao titular a opção de exercer o direito de receber volumes maiores ou menores, de acordo com o mercado. Neste artigo, o preço do GN é a principal fonte de incerteza e foi modelado com um processo estocástico seguindo o modelo de dois fatores de Schwartz e Smith (2000) ao qual foi incorporada a sazonalidade trimestral. Para estimar os preços à vista do GN, usando os preços dos contratos futuros do Henry Hub, implementou-se o filtro de Kalman. O apreçamento da opção foi realizado através do modelo de árvore binomial bivariável desenvolvido por Hahn e Dyer (2011). O valor da opção de swing foi positivo nos dois casos analisados, mostrando que essa opção tem valor e deve ser analisada para inclusão nos contratos de GN. As características do contrato analisado foram as mesmas especificadas em Jaillet, Ronn e Tompaidis (2004).
Palavras-chave
Finanças. Derivativos. Precificação de contratos. Processos estocásticos
Abstract
In the natural gas (NG) market, contracts incorporate flexibility in the volume of the product. These contracts are known as swing options. Such contracts allow the option holder to exercise the right to receive greater or smaller amounts of NG contracted in accordance with market. Variation in the price of NG, which is the main source of uncertainty, was modeled in this study as a stochastic process using the two-factor model of Schwartz and Smith (2000), which was incorporated into assessment of the quarterly seasonality. To estimate NG spot prices using the Henry Hub prices of futures contracts traded on the NYMEX, it was necessary to implement the Kalman filter. The pricing of the option was conducted using the binomial tree model bi-variable developed by Hahn and Dyer (2011). The value of the swing option was positive in both cases analyzed, indicating that this option should be considered for inclusion in NG contracts. The characteristics of the analysis were the same as those specified in Jaillet, Ronn and Tompaidis (2004).
Keywords
Finance. Derivatives. Contracts pricing. Stochastic processes
References
ADLAND, R.; JIA, H.; LU, J. Price dynamics in the market for Liquid Petroleum Gas transport. Energy Economics, v. 30, n. 3, p. 818-828, 2008. http://dx.doi.org/10.1016/j.eneco.2007.02.008
AIUBE, F. A. L. Modelos quantitativos em finanças com enfoque em commodities. Porto Alegre: Bookman, 2013.
AIUBE, F.; BAIDYA T.; TITO, E. Analysis of commodity prices with the particle filter. Energy Economics, v. 30, n. 2, p. 597-605, 2008. http://dx.doi.org/10.1016/j.eneco.2006.06.006
AGÊNCIA NACIONAL DE ENERGIA ELÉTRICA - ANEEL. Disponível em:
AGÊNCIA NACIONAL DO PETRÓLEO, GÁS NATURAL E BIOCOMBUSTÍVEIS – ANP. Indústria Brasileira de Gás Natural: Regulação Atual e Desafios Futuros. Rio de Janeiro: ANP, 2001. (Série ANP, n. 2).
BALDVINSDÓTTIR, E. K.; PALMBORG, L. On constructing a market consistent economic scenario generator. Sweden: Seminars Matematical Statistics KTH, 2011. PMid:22057365.
BANCO CENTRAL DO BRASIL. Ata do Compo, Maio/2012, 167º Reunião, publicada em 8/06/2012. BCB, 2012.
BASTIAN-PINTO, C. L.; BRANDÃO, L. E. T.; HAHN, W. J. Flexibility as a source of value in the production of alternative fuels: The etanol case. Energy Economics, v. 31, n. 3, p. 411-422, 2009. http://dx.doi.org/10.1016/j.eneco.2009.02.004
BLACK, F.; SCHOLES, M. The pricing of options and corporate liabilities. Journal of Political Economy, v. 81, n. 3, p. 637-659, 1973. http://dx.doi.org/10.1086/260062
BOYLE, P. A. A Lattice Framework for option pricing with two state variables. Journal of Financial an Quantitative Analysis, v. 23, n. 1, p. 1-12, 1988. http://dx.doi.org/10.2307/2331019
BRENNAN, M. J.; SCHWARTZ, E. S. Evaluating natural resource investment. Journal of Business, v. 58, n. 2, p. 135-157, 1985. http://dx.doi.org/10.1086/296288
BRANDÃO, L. E. T.; DYER, J. S. Projetos de opções reais com incertezas correlacionadas. Base-Revista de Administração e Contabilidade da Unisinos, v. 6, n. 1, p. 19-26, 2009. http://dx.doi.org/10.4013/base.2009.61.02
BRANDÃO, L. E. T.; HAHN, W. J.; DYER, J. S. Using binomial decision trees to solve real options valuation problems. Decision Analysis, v. 2, n. 2, p. 69-88, 2005. http://dx.doi.org/10.1287/deca.1050.0040
BRASIL. Ministério de Minas e Energia. Resenha Energética Brasileira (2011). Brasília: MME, 2011.
BRIGO, D.; MERCURIO, F. Interest rate models – theory and practice with smile, inflation and credit. New York: Springer Finance – Verlag Berlin Heidelberg, 2010.
CARTEA, A.; WILLIAMS, T. UK Gas Market: the market price of risk and applications to multiple interruptible supply contracts. Energy Economics, v. 30, n. 3, p. 829-846, 2008. http://dx.doi.org/10.1016/j.eneco.2007.03.001
CLEWLOW, L.; STRICKLAND, C. Valuing energy options in a one factor model fitted to forward prices. Sydney: Work Paper, School of Finance and Economics, University of Technology, 1999.
CORTAZAR, G.; NARANJO, L. An N-factor gaussian model of oil futures prices. Journal of Futures Markets, v. 26, n. 2, p. 243-268, 2006. http://dx.doi.org/10.1002/fut.20198
COX, J. C.; ROSS, S. A.; RUBINSTEIN, M. Option Pricing: a simplified approach. Journal of Financial Economics, v. 7, n. 3, p. 229-263, 1979. http://dx.doi.org/10.1016/0304-405X(79)90015-1
FIGUEROA, M. Pricing multiple interruptible-swing contracts. Birkbeck: University of London, Working Papers in Economics & Finance, 2006.
GÁS NET. O site do gás natural. Disponível em:
GIBSON, R.; SCHWARTZ, E. Stochastic convenience yield and pricing of oil contingent claims. Journal of Finance, v. 45, n. 3, p. 959-976, 1990. http://dx.doi.org/10.1111/j.1540-6261.1990.tb05114.x
GUIGUES, V.; SAGATIZABAL, C.; ZUBELLI, J. P. Robust management and pricing of LNG contracts with cancellation options. IMPA, 2010.
HAFF, I. H.; LINDQVIST, O.; LøLAND, A. Risk Premium in the UK Natural Gas Forward Market. Energy Economics, v. 30, n. 5, p. 2420-2440, 2007. http://dx.doi.org/10.1016/j.eneco.2007.12.002
HAHN, W. J. A Discrete-time approach for valuing real options with underlying mean-reverting stochastic processes. 2005. Dissertation (Masterâs Degree)-University of Texas, Austin, 2005.
HAHN, W. J.; DYER, J. S. Discrete time modeling of mean-reverting stochastic processes for real option valuation. European Journal of Operational Research, v. 183, n. 2, p. 534-548, 2008. http://dx.doi.org/10.1016/j.ejor.2006.11.015
HAHN, W. J.; DYER, J. S. A discrete time approach for modeling two-factor mean-reverting stochastic processes. Decision Analysis, v. 8, n. 3, p. 220-232, 2011. http://dx.doi.org/10.1287/deca.1110.0209
HAMBLY, B.; HOWISON, S.; KLUGE, T. Modelling spikes and pricing swing options in electricity markets. Quantitative Finance, v. 9, n. 8, p. 937-949, 2008. http://dx.doi.org/10.1080/14697680802596856
HARRISON, J.; KREPS, D. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, v. 20, n. 3, p. 381-408, 1979. http://dx.doi.org/10.1016/0022-0531(79)90043-7
HARRISON, J.; PLISKA, S. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications, v. 11, p. 215-260, 1981. http://dx.doi.org/10.1016/0304-4149(81)90026-0
HEM, O. D. et al. The option to switch from oil to natural gas in active offshore petroleum fields. In: ANNUAL INTERNATIONAL CONFERENCE REAL OPTIONS THEORY MEETS PRACTICE, 15., 2011, Turku. Proceedings... ROG, 2011.
HULL, J.; WHITE, A. Numerical procedures for implementing term structure models I. Journal of Derivatives, v. 2, n. 1, p. 7-16, 1994a. http://dx.doi.org/10.3905/jod.1994.407902
HULL, J.; WHITE, A. Numerical procedures for implementing term structure models II. Journal of Derivatives, v. 2, n. 2, p. 37-42, 1994b. http://dx.doi.org/10.3905/jod.1994.407908
JAILLET, P.; RONN, E. I.; TOMPAIDIS, S. Valuation of Commodity-Based Swing Options. Management Science, v. 50, n. 7, p. 909-921, 2004. http://dx.doi.org/10.1287/mnsc.1040.0240
LUCIA, J. J.; SCHWARTZ, E. S. Electricity Prices and Power Derivatives: evidence from the Nordic Power Exchange. Review of Derivatives Research, v. 5, n. 1, p. 5-50, 2001. http://dx.doi.org/10.1023/A:1013846631785
MANOLIU, M.; TOMPAIDIS, S. Energy Futures Prices: Term Structure Models with Kalman Filter Estimation. Applied Mathematical Finance, v. 9, n. 1, p. 21-43, 2000. http://dx.doi.org/10.1080/13504860210126227
MAROTTA, L. L. S. Calibração do Modelo de Schwartz-Smith com Filtro de Kalman. 2011. Dissertação (Mestrado em Métodos Matemáticos em Finanças)-Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, 2011.
MATHIAS, M. C. P. P. A formação da indústria global de gás natural: definição, condicionantes e desafios. 2008. Tese (Doutorado em Ciências em Planejamento Energético)-Universidade Federal do Rio de Janeiro, Rio de Janeiro, 2008.
NELSON, D. B.; RAMASWAMY, K. Simple binomial processes as diffusion approximations n financial models. Review of Financial Studies, v. 3, n. 3, p. 393-430, 1990. http://dx.doi.org/10.1093/rfs/3.3.393
PARK, F. C. Scenario analysis for bond and loan portfolios. Capital Markets & Portfolio Research, Inc., 2003.
PARSONS, C. Valuing commodity storage contracts: a two-factor tree approach. WTM Energy Software, LLC, 2007.
PETROBRAS. Relatório de Atividades 2012. Rio de janeiro: Petrobras, 2012.
PINTO, C. L. B. Modelagem de opções reais com processos de reversão à média em tempo discreto: uma aplicação na Indústria Brasileira de Etanol. 2009. Tese (Doutorado)-Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, 2009.
SCHWARTZ, E. The stochastic behavior of commodity prices: implications for valuation and hedging. Journal of Finance, v. 52, n. 3, p. 923-973, 1997. http://dx.doi.org/10.1111/j.1540-6261.1997.tb02721.x
SCHWARTZ, E.; SMITH, J. Short-Term Variations and Long-Term Dynamics in Commodity Prices. Management Science, v. 46, n. 7, p. 893-911, 2000. http://dx.doi.org/10.1287/mnsc.46.7.893.12034
SIMÕES, M. D. P. et al. Opções de Swing no Mercado Brasileiro de Energia Elétrica. Revista de Economia e Administração, v. 10, n. 4, p. 591-610, 2011.
SøRENSEN, C. Modeling Seasonality in Agricultural Commodity Futures. Journal of Futures Markets, v. 22, n. 5, p. 393-426, 2002. http://dx.doi.org/10.1002/fut.10017
TSENG, C.; LIN, K. A Framework Using Two-Factor Price Lattices for Generation Asset Valuation. Operations Research, v. 55, n. 2, p. 234-251, 2007. http://dx.doi.org/10.1287/opre.1060.0355
ZHANG, B.; OOSTERLEE, C. W. An efficient pricing algorithm for swing options based on fourier cosine expansions. Reports of the Department of Applied Mathematical Analysis, Delft University of Technology, The Netherlands, 2010.