A Multi-Factor Forward Price Model for Network-Based Commodities

We introduce a multi-factor forward price model for network-based.commodities such as point-to-point telecommunications capacity. The model explicitly includes network effects and the requirement that tradeables (forward contracts) be martingales under an appropriate measure. In essence the forward price model is a combination of network optimization and mathematical finance. The model is based on a modified HJM approach with additional compensators to include network effects and the martingale requirement. We show that the combination of network effects and martingale requirements on forward contract prices changes price volatility, observed standard deviations and, consequently, option prices. The effect of the network is always significant but the importance of the topology itself is variable. For typical volatilities European call option values are roughly 10% less in a network context for 1 year maturities for at-the-money and above strike prices. The significance for more exotic and specially designed options, e.g. alternative-path barrier options, may be very much higher.