Narrow Results

We present a fast method to price and hedge CMS spread options in the displaced-diffusion co-initial swap market model. Numerical tests demonstrate that we are able to obtain sufficiently accurate prices and Greeks with computational times measured in milliseconds. Further, we find that CMS spread options are weakly dependent on the at-the-money Black implied volatility skews.

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra (VMV) process dynamics. Such a price dynamics is particularly relevant in energy markets, modeling for example the spot price of power and gas. VMV processes are in general not semimartingales, but contain several special cases of interest in energy markets, like for example continuous-time autoregressive moving average processes. Based on a change of measure, we obtain a pricing expression based on a univariate Fourier transform of the payoff function and the characteristic function of the price dynamics. Moreover, the spread option price can be expressed in terms of the forward prices on the underlying dynamics assets. We compute a linear system of equations for the quadratic hedge for the spread option in terms of a portfolio of underlying forward contracts.

This paper introduces a methodology of analytical approximation in general European option-pricing case based on local volatility model and then apply it to price a European Spread Option. The approximation procedure is flexible in pricing financial derivatives with any form of volatility, drift rate, risk-free rate and payoff function. We also work out the explicit pricing formula up to the second-order approximation of spread option which is good-fitting compared with finite difference method and Monte Carlo simulation. The relative error compared to finite difference method is no more than 5%, which attests to the accuracy of our second-order closed-form formulas.