The term multifactor model is very broad, encompassing any modeling framework in which multiple stochastic processes, often correlated Brownian motions, drive a set of asset prices. We know from the factor analysis in Chapter 5 that the volatility of the second PCA factor is certainly present, with a volatility of roughly 20 percent of that of the first factor for crude oil and natural gas. This would suggest that structures with nonlinear dependence on multiple forward prices will require something more than a single Brownian motion. Moreover, single-factor models do not provide the flexibility required to unify and synthesize closely related market data.

Consider the following questions:

1. • How should we value more complex structures in which the payoff depends explicitly on the joint dynamics of many forward prices? These can arise in relatively simple settings such as strips of “vanilla” options structures with a total capped payout (TARN structures) or more complex situations such as natural gas storage, which requires a control theoretic framework applied to the entire forward curve.

2. • How do we accommodate the broad separation of time scales in price dynamics from “long-wavelength” features in which the entire forward curve moves in tandem (think of the first factor) to spot price dynamics? For example, in power, price dynamics is driven by factors with characteristic time scales of the order of a few days.

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