Abstract
The presence of optionality in the generation and transmission of power means that valuing physical and financial assets requires using option theory, which in turn requires studying stochastic processes appropriate for the description of power prices. Power prices are much more volatile than other commodity prices and exhibit interesting behavior such as regime switching between normal and spiked states. The probability distributions underlying such stochastic process provide an input for price forecasts, which are based on price history. They also provide an input into valuation of transmission and transmission options in cases where the implied market-based measures of volatilities and correlations are lacking. Combining information from this analysis of stochastic processes for power prices with the Black–Scholes framework for option valuation, specifically using that framework to calculate the value of spread options, yields methods for calculating the value of transmission as well as for calculating the value of financial transmission options, which also depend on spread of power prices. The three main techniques for obtaining the option value include analytical approaches, binomial-type trees (finite difference methods), and Monte Carlo simulations. Each of these techniques presented in the paper has its own advantages and disadvantages and is complementary to the other two, providing independent validation and quality control for transmission valuation algorithms.
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References
Acton FS (1970) Numerical methods that work. Harper and Row, New York
Alexander C, Scourse A (2004) Bivariate normal mixture spread option valuation. Quant Finance 4:637–648
Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press, Cambridge
Baronblatt GI (2003) Scaling. Cambridge University Press, Cambridge
Baron MI (2002) Bayes and asymptotically pointwise optimal stopping rules for the detection of influenza epidemics. In: Gatsonis C, Kass RE, Carriquiry A, Gelman A, Higdon D, Pauler DK and Verdinelli I (eds) Case studies of bayesian statistics, vol. 6. Springer, New York
Baron M (2004) Sequential methods for multistate processes. In: Mukhopadhyay N, Datta S and Stattopadhyay S (eds). Application of sequential methodologies. Marcel Dekker, New York
Baron M, Rosenberg M, Sidorenko N (2001) Modelling and prediction with automatic spike detection. Energy Power Risk Manage 36–9
Baron M, Rosenberg M, Sidorenko N (2002) Divide and conquer: forecasting power via automatic price regime separation. Energy Power Risk Manage 70–3
Basseville M, Nikiforov IV (1993) Detection of abrupt changes: theory and application. PTR Prentice-Hall, Englewood Cliffs
Bjork T (2004) Arbitrage theory in continuous time, 2nd edn. Oxford University Press, Oxford, UK
Black F (1976) The pricing of commodity contracts. J Financ Econ 3:167–179
Bridges CB, Winquist AG, Fukuda K, Cox NJ, Singleton JA, Strikas RA (2000) Prevention and Control of Influenza, Morbidity and Mortality Weekly Reports, Centers for Disease Control and Prevention, 49:1–38
Bridgman PW (1931) Dimensional analysis. Yale University Press, New Haven
Brockwell PJ, Davis RA (2nd printing edition, 2009), (1991) Time series: theory and methods. Springer, New York
Buckingham E (1914) On physically similar systems; illustration of the use of dimension equations. Phys Rev 4:345–376
Calvin WH (2002) A brain for all seasons: human evolution and abrupt climate change. University of Chicago Press, Chicago, IL
Carlin BP, Louis TA (2008) Bayesian methods for data analysis, 3rd edn. Chapman & Hall/CRC, Boca Raton, FL
Carmona R, Durrleman V (2003) Pricing and hedging spread options. SIAM Rev 45(4):627–685
Cherubini U, Luciano E (2002) Bivariate option pricing using copulas. Appl Math Finance 9:69–86
Clewlow L, Strickland C (1998) Implementing derivatives models. Wiley, New York
Clewlow L, Strickland C (1999) Energy derivatives: pricing and risk management. Lacima
Cloth P, Backofen R (2000) Computational molecular biology. Wiley, Chichester, England
Dahlquist G, Bjork A (1974) Numerical Methods (trans: Anderson N). Prentice-Hall, Englewood Cliffs, NJ
Dixit AK, Pindyck RS (1994) Investment under uncertainty. Princeton University Press, Princeton, NJ
Durbin S, Eddy S, Krogh A, Mitchison G (1998) Biological sequence analysis. Probabilistic models of proteins and nucleic acids. Cambridge University Press, Cambridge MA
Embrechts P, McNeil A, Straumann D (1999) Correlation: pitfalls and alternatives. Risk 12:69–71
Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, New York
Granott N, Parziale J (2002) Microdevelopment: A process-oriented perspective for studying development and learning. In: Granott N and Parziale J (eds) Microdevelopment: Transition processes in development and learning. Cambridge University Press, Cambridge, pp. 1–28
Gregoire V, Genst C, Gendron M (2008) Using copulas to model price dependence in energy markets. Energy Risk 5:58–64
Hull JC (2002) Options, futures, and other derivatives, 5th edn. Prentice-Hall, Upper Saddle River, NJ
Jackel P (2002) Monte Carlo methods in finance. Wiley, New York
Judd KL (1998) Numerical methods in economics. MIT, Cambridge, MA
Kamrad B, Ritchken P (1991) Multinomial approximating models for options with k state variables. Manage Sci 37(12):1640–1652
Khan R (2009) Distributional properties of CUSUM stopping times and stopped processes. Sequential Anal 28(2):175–187
Kloeden PE, Platen E (1994) Numerical solution of stochastic differential equations through computer experiments. Springer, New York
Lai TL (1995) Sequential changepoint detection in quality control and dynamical systems. J R Stat Soc B 57:613–658
Lai TL (2001) Sequential analysis: some classical problems and new challenges. Stat Sin 11: 303–408
Margrabe W (1978) The value of an option to exchange one asset for another. J Finance 33: 177–186
Merton RC (1976) Option pricing when underlying stock returns are discontinuous. J Financ Econ 3:125–144, reprinted in Merton RC, Continuous Time Finance, Blackwell, Oxford, 1990
Montgomery DC (1997) Introduction to statistical quality control, 3rd edn. Wiley, New York
Piaget J (1970) Piaget’s theory, In: Mussen PH (ed) Carmichael’s manual of child psychology. Wiley, New York, pp. 703–732
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd edn. Cambridge University Press, Cambridge
Papalexopoulos A, Treinen R (2005) Important practical considerations in designing an FTR market. Presented at the IEEE PES Meeting, St. Petersburg, Russia
Rabiner LR (1989) A tutorial on Hidden Markov Models and selected applications in speech recognition. IEEE Proc 77:257–285
Ronn EI (2002) Introduction. In: Ronn EI (ed) Real options and energy management: using options methodology to enhance capital budgeting decisions. Risk Books, London
Rosenberg M, Bryngelson JD, Sidorenko N, Baron M (2002a) Price spikes and real options: transmission valuation, In: Ronn EI (ed) Real options and energy management: using options methodology to enhance capital budgeting decisions. Risk Books, London
Rosenberg M, Bryngelson JD, Baron M (2002b) Probability and stochastic calculus: review of probability concepts, In: Ronn EI (ed) Real options and energy management: using options methodology to enhance capital budgeting decisions. Risk Books, London
Spokoiny V (2009) Multiscale local change point detection with applications to value-at-risk. Ann Stat 37(3):1405–1436
Shreve S (2004) Stochastic calculus for finance II: continuous time models. Springer, New York
Stoer J, Bulirsch R (1980) Introduction to numerical analysis. Springer, Berlin
Tavella D (2002) Quantitative methods in derivative pricing. Wiley, New York
Wilson EB (1990) An introduction to scientific research. Dover, New York
Zacks S (2009) Stage-wise adaptive designs. Wiley, Hoboken, NJ
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Rosenberg, M., Bryngelson, J.D., Baron, M., Papalexopoulos, A.D. (2010). Transmission Valuation Analysis based on Real Options with Price Spikes. In: Rebennack, S., Pardalos, P., Pereira, M., Iliadis, N. (eds) Handbook of Power Systems II. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12686-4_4
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