The Schwartz–Smith model writes the log spot price as the sum of a short-term deviation , an Ornstein–Uhlenbeck process reverting to zero at speed with volatility , and a long-term level , a Brownian motion with volatility , the two correlated by . Its forward curve moves as
so that with the variance. Seasonality sits in the initial curve , which the model fits exactly.
Voorbeelden
Example 16.2 (Calibration)
An illustrative Henry Hub-like curve runs from 2.60 dollars for April to 3.50 for January. Options expiring half a month before each delivery are quoted at implied volatilities falling from 62.0% (May) to 43.0% (March), synthetic. With fixed, a Levenberg–Marquardt fit gives , and .