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We derive the price of a spread option based on two assets which follow abivariate volatility modulated Volterra process dynamics. Such a price dynamicsis particularly relevant in energy markets, modelling for example the spotprice of power and gas. Volatility modulated Volterra processes are in generalnot semimartingales, but contain several special cases of interest in energymarkets like for example continuous-time autoregressive moving averageprocesses. Based on a change of measure, we obtain a pricing expression basedon a univariate Fourier transform of the payoff function and the characteristicfunction of the price dynamics. Moreover, the spread option price can beexpressed in terms of the forward prices on the underlying dynamics assets. Wecompute a linear system of equations for the quadratic hedge for the spreadoption in terms of a portfolio of underlying forward contracts.

Pricing and hedging of energy spread options and volatility modulated Volterra processes