Production
https://prod.org.br/doi/10.1590/S0103-65132013005000084
Production
Article

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

Downloads: 0
Views: 816

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: . Acesso em: 18 jan. 2012.

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: . Acesso em: 15 jan. 2012.

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 (Master’s 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.
5883a4527f8c9da00c8b4898 production Articles
Links & Downloads

Production

Share this page
Page Sections