## Forward Curve

Energy prices do not necessarily follow the same behaviour as other financial assets. Let $F(t,T)$ denote the forward price at time t for settlement at time $T$. The (initial) forward price curve $F(0,T)$ is specified at discrete settlement dates $T_1,...,T_m$. Linear interpolation is used for other settlement dates T and:

,

where $i$ is either the least index for which $T_i \ge T$, or $i=m$ if $T \gt T_m$.

## CSForwardPriceModel

For commodity/Energy deals, the Forward price is modeled directly. For each settlement date T, the SDE for the forward price is:

Where:

• $\mu$ is the drift rate
• $\sigma$ is the volatility
• $\alpha$ is the mean reversion speed
• $W(t)$ is the standard Weiner Process

Final form of the model is

Where $Y$ is a standard Ornstein-Uhlenbeck Process with variance:

The spot rate is given by