Swaption Pricing under Libor Market Model Using Monte-Carlo Method with Simulated Annealing Optimization

Abstract

The thesis seeks to use simulated annealing optimization to minimize the difference between the value of the libor model volatility and the ones quoted in the market for congruent pricing of a Swaption contract. The simulated annealing optimization technique, being a global minimisation method, would provide accurate parameters that will simulate libor rates that are harmonious with the observed yield curve. This latter feature employed in a Monte-Carlo pricing method would price the Swaption contract fundamentally closer to its market value than other local optimization methods. The SA method starts from an initial point, often random, then searches the neighbourhood of the current solution for the next point. The neighbourhood function search is in accordance with the set probabilistic distribution that will determine the distance between the two solutions. Each solution has a cost value associated with it. The cost function determines the eligibility of the solution by measuring its discrepancy with the set limit. If the discrepancy is larger than the set limit, a new solution is sought. If the discrepancy is still large, the old and new cost value is compared, and the latter is accepted if it’s less than the former or otherwise rejected with a certain probability that is largely dependent on the control mechanism. The method terminates if the cost value attained is equal to the set tolerance level. Different from other heuristic methods that solely base their solution on the iterative improvement of the solution’s cost value, simulated annealing accepts some inferior solutions so as to have a wider search in the design space. The main advantage of the method is the ability to escape local minimum entrapment through the aforementioned acceptance/rejection criteria. The results indicate that the advantageous aspects of the Simulated annealing enable it to outperform the least square non-linear optimization method commonly used in the simulation.