Specialeforsvar ved Christian Sehested Hansen

pecialeforsvar ved Christian Sehested Hansen

Title: Closed-form solution for Swaptions. 

Resume:  It is impossible to achieve a closed-form solution for swaptions using forward rates in the LIBOR market model. Therefore, pricing swaptions in the LIBOR market model is done by approximation. The approximation assumes that the forward swap rate and LIBOR rate are both log-normally distributed, which is impossible. Therefore, a different market model might improve the pricing of swaptions. Gourion introduced a new market model, the Continuous Forward Market (CFM) rate model, in his paper (Gourion 2024), which claims to have a closed-form solution for swaptions.

This thesis will show that the closed-form solution for pricing swaptions Gourion arrived at is an approximation. This thesis will derive the Euler discretization for the CFM and work on implementing the Monte Carlo method. The implementation's goal is to calculate the implied volatility of caplets and swaptions. Furthermore, we will investigate the effect of Gourion's approximation on the implied volatility of the swaptions. We will implement the LIBOR market model using Euler discretization and the Monte Carlo method to test the effect of the approximation made in the LMM under the terminal forward measure.

The result of the implementations in the CFM model observes a decrease in implied volatility when the tenor length increases. However, the results of the test remain inconclusive due to a problem with the implementation.\\\\
The test of the implied volatilities in the LIBOR market model under the terminal measure shows that the approximations in the LIBOR market model are acceptable when the model is not stress-tested. Due to the stress test's exacerbating the errors in implied volatility, introduced by the approximations

Vejleder: David Skovmand
Censor: Bjarne Astrup Jensen