Caporin, Massimiliano and Pres, Juliusz and Torro, Hipolit (2010): Model based Monte Carlo pricing of energy and temperature quanto options.
Download (499kB) | Preview
Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the Black-Scholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.
|Item Type:||MPRA Paper|
|Original Title:||Model based Monte Carlo pricing of energy and temperature quanto options|
|Keywords:||weather derivatives; Quanto options pricing; derivative pricing; model simulation; forecast|
|Subjects:||L - Industrial Organization > L9 - Industry Studies: Transportation and Utilities > L94 - Electric Utilities
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q5 - Environmental Economics > Q54 - Climate; Natural Disasters; Global Warming
|Depositing User:||Hipòlit Torró|
|Date Deposited:||03. Oct 2010 00:41|
|Last Modified:||12. Feb 2013 05:27|
Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O., 1996, Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 3–30.
Bauwens, L., Laurent, S., and Rombouts, J.V.K., 2006, Multivariate GARCH Models: A Survey, Journal of Applied Econometrics, 21, 79-110.
Benth, F. E., and Benth, J. S. (2007) The volatility of temperature and pricing of weather derivatives. Quantitative Finance, 7(5), 553-561.
Benth, F. E., Koekebakker S. and Ollmar, F. (2007). Extracting and Applying Smooth Forward Curves from Average-Based Commodity Contracts with Seasonal Variation. Journal of Derivatives 15(1), 52-66.
Black, F., and Scholes, M., 1973, The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.
Bollerslev, T., 1986, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307–327.
Bollerslev, T., 2009, Glossary to ARCH (GARCH), in Watson, M., Bollerslev, T., and Russell, R. (eds.), Volatility and Time Series Econometrics, Essays in Honor of Robert Engle, Oxford University Press
Bollerslev, T., Chou, R.Y., and Kroner, K.F., 1992, ARCH modeling in finance: a review of the theory and empirical evidence, Journal of Econometrics, 52, 5–59.
Bollerslev, T., Engle, R.F., and Nelson, D.B., 1994, ARCH models, in Handbook of Econometrics, Engle. R., and McFadden, D. (eds), North Holland Press, Amsterdam.
Bordignon, S., Caporin, M., and Lisi, F., 2007, Generalized long-memory GARCH models for intra-daily volatility, Computational Statistics and Data Analysis, 51, 5900-5912.
Bordignon, S., Caporin, M., and Lisi, F., 2009, Periodic long-memory GARCH models, Econometric Reviews, 28-1, 60-82. Bossley L., 2004, A fair wind, Petroleum Economist, January 2004, 34.
Brix, A., S. Jewson and C. Ziehmann , 2005, Weather Derivative Valuation, The meteorological, statistical, financial and mathematical foundations, Cambridge University Press
Campbell, S.D. and F.X. Diebold, 2005, Weather forecasting for weather derivatives, Journal of the American Statistical Association, 100-469, 7-16
Cao, M., and Wei, J., 2000, Pricing the weather. Risk, 13-5, 67–70.
Cao, M. and Wei, J., 2004, Weather derivatives valuation and market price of weather risk, Journal of Future Markets, 24, 1065-1090.
Christodoulakis, G.A., and Satchell, S.E., 2002, Correlated ARCH: modelling the time-varying correlation between financial asset returns, European Journal of Operations Research, 139, 351–370.
Davis, M., 2001, Pricing weather derivatives by marginal value, Quantitative Finance, 1, 1-14. Dischel, R.S. (Ed.), 2002, Climate risk and the weather market: financial risk management with weather hedges, Risk Publications, London.
Engle, R.F., 1982, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987–1007.
Engle, R.F., 2002, Dynamic conditional correlation, a simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 20, 339–350.
Escribano, A., Peña, J. I., and Villaplana, P. (2002) Modelling Electricity Prices: International Evidence. Universidad Carlos III, Economics Series 08, Working Paper 02-27.
Gibson, R., and Schwartz, E. S. (1990) Stochastic convenience yield and the pricing of oil contingent claims. The Journal of Finance, 65(3), 959-976.
Henderson, R., 2002, Pricing Weather Risk, in Weather Risk Management, Markets, Products and Applications, ed. Banks E., 167-196.
Ho, T.S., Stapleton, R.C., and Subrabmanyan, M.G., 1995, Correlation Risk, Cross-market Derivative Products and Portfolio Performance, Journal of European Financial Management, Vol. 1, No. 2, 105-124.
Hull, J. C. (1997) Options, futures and other derivatives. Third Edition. Prentice-Hall International Inc., London.
Koopman, S. J., Ooms, M., and Carnero, M. A. (2007). Periodic heteroskedastic reg-ARFIMA- GARCH models for daily electricity prices. Journal of the American Statistical Association 102, 16–27.
Lucia, J.J. and E.S. Schwartz (2002). Electricity prices and power derivatives: Evidence from the Nordic Power Exchange. Review of Derivatives Research, 5, 5-50.
McCallion, P., 2009, Umbrella Coverage, Energy Risk, September 2009, 42-45.
Nelken, I., 2000, Weather Derivatives – Pricing and Hedging, Super Computer Consulting, Inc. IL. USA , January.
Pirrong, C., and Jermakyan, M. (2008) The price of power: The valuation of power and weather derivatives. Journal of Banking and Finance, 32. 2520-2529.
Rickels, W., Duscha, V., Andreas K. and Peterson S. (2007). The determinants of allowance prices in the European Emissions Trading Scheme - Can we expect an efficient allowance market 2008? Kiel Institute for The World Economy, Working Paper No 1387.
Silvennoinen, A., and Terasvirta, T., 2009, Multivariate GARCH models, in Andersen, T.G., Davis, A.R., Kreiß, J., and Mikosch, T. (eds.), Handbook of Financial Time Series, Springer
Tse, Y.K., and Tsui, A.K.C., 2002, A multivariate GARCH model with time-varying correlations, Journal of Business and Economic Statistics, 20, 351–362.
VanderMarck, P., 2003, Marking to model or to market? Environmental Finance, 1, pp.36-38.
Weinstein, J., 2001, Carbon-denominated weather swaps, Environmental Finance, London, No 11, 2001.
Weron, R., Simonsen I. and Wilman P. (2004). Modelling highly volatile and seasonal markets: evidence from the Nord Pool electricity market. In H. Takayasu (editor), Procedings of the second Nekkei Econophysics symposium – Application of Econophysics 2002, 182-191, Springer.
Wolak, F. (1999). Market design and price behavior in restructured electricity markets. An international comparison. In Ito, T. and Krueger, A. (ed.), Competition Policy in the Asia Pacific Region, EASE Volume 8, University of Chicago Press, 79-134.
Zhang, P.G., 2001, Exotic Options. A Guide to Second Generation Options, World Scientific, Singapore 2001.
Zeng, L., 2000, Weather derivatives and weather insurance: concept application and analysis, Bulletin of the American Meteorological Society, 81, 2075-2982.