Volume 3 — Valuation and Risk Metrics © Copyright 2002, CCRO. All rights reserved. 43 APPENDIX C– EXAMPLE MODELS FOR VALUING COMMODITIES TRANSACTIONS This appendix provides a short list of the types of models that can be used to calculate the value and quantify the risk of some business activities. The list is by no means comprehensive, nor do we suggest that the use of the models listed here is necessarily best practice for a given type of transaction. The actual model that is used and the level of abstraction that is used should be a function of the size and complexity of the transaction and level of value and risk that is at stake for the company. Individual companies may choose to use variations of these models or to use different models altogether. Spread Approximation Model This model uses the Black model, which is a Black-Scholes closed-form option pricing model modified for European options on forwards. Like the Black-Scholes model, it assumes a geometric Brownian motion price process whereby the percentage of price changes is random and normally distributed. The model values options, so there is no economic arbitrage with futures contracts (after considering the risk-free interest rate). Power The spread approximation option evaluation model is used to value electric tolling deals whereby generation supplies electricity to the customer who pays for natural gas. These deals are generally less than 7 years in duration. The spark-spread model approximates a European call spread between gas and electricity prices using the Black valuation formula. The model is used to compute expected monthly option values, with some consideration of daily optionality emphasizing the near term. The optionality is divided between peak and off-peak power pricing periods. • The model’s inputs are: − Forward power and delivered natural gas prices − Contract/unit capacity, variable O&M cost/MWh, heat rate − Forward power and gas volatilities − Correlation between power and gas prices − Contract pricing − Risk-free discount rates and risk premium • The model’s outputs are: − Monthly intrinsic and extrinsic option values − Monthly NPV of fixed payments − Mark-to-market value by month