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These papers are related to modelling options and stochastic processes. Option trading strategies based on forecast volatility are in a different section.

#### **Risk-Neutral Stochastic Processes for Commodity Derivative Pricing: An

#### Introduction and Survey

Author: Duane Seppi

Published: Real Options and Energy Management. Risk Publications 2002

(I don't have an electronic copy, but a paper copy is in the BACK of my financial engineering course packet)

Keywords: Stochastic processes, RN valuation, energy / commodity derivatives

Introduces risk-neutral valuation, where E(payoff) / (1 + RAD) = E^RN(payoff) / (1 + r_f), and RAD is the [unknown] risk-adjust discount rate, r_f is the risk-free rate, and E^RN is an expectation of the risk-neutral process. The difference between the RN and real dynamics is the price-of-risk adjusment. Defines an asset as claim on future CF, so electricity is NOT an asset, so it has no expected return

Shows the commodities exhibit seasonality, mean reversion, and high short-term but low long-term implied volatility (due to mean reversion). Says the forward prices are the RN expectation of future spot prices, and RN dynamics of future prices are a random walk (I don't get this part). Notes that geometric brownian motion (GBM) gives bad commodity price dynamics. Even if the GBM is calibrated with a varying dividend yield and volatility function to match observed option prices, it still implies that a shock to today's stock price moves the entire future price path up, which isn't the case: true mean reversion is needed. He notes that, even if two models give the same option prices for options to which they were calibrated, they can give different hedging parameters and different prices for other (esp. exotic) options [he calls this model risk]

Next he covers other models, like mean-reverting jump diffusion, which doesn't allow perfect hedging. He also covers multi-factor models, with two underlying weiner processes, again preventing perfect hedging, and structural models, which model supply and demand curves and changes in price and quantity related to these. Lastly he covers HJM (Heath Jarrow Morton) models where the entire futures price curve is modeled, with sensitivity to many varying factors (given by principle components analysis or explicitly specified). Then future spot prices are modeled as realized futures prices: S_T = S_0 + integral_0^T[ dF_t ]