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Description:
Robert Leon
This research paper presents an approximation for the price of CMS spread options using the swap market model. In the swap market model, the assumption about the underlying swap rate processes is that they are lognormal under the relevant measure, this being the annuity measure or Present Value of a Basis Point (PVBP). To price European options, the measure associated with the zero-coupon bond maturing at the expiry of the option is the most convenient. We will derive the stochastic differential equations for the swap rates under this measure. The resulting drift is a function of the swap rates and their covariance structure. Hence, the drift is stochastic. The approximation that we will implement is to assume lognormality. This is done by setting the swap rates that appear in the drift to their current values so that the drift is no longer stochastic, termed