Ant Colony Optimization for Option Pricing

Summary

Option pricing is one of the fundamental problems in finance. This chapter proposes a novel idea for pricing options using a nature inspired meta-heuristic algorithm called Ant Colony Optimization (ACO). ACO has been used in many NP-hard combinatorial optimization problems and most recently in self-organized environments in dynamic networks such as ad hoc and sensor networks. The dynamic changes in financial asset prices poses greater challenges to exercise the option at the right time. The dynamic nature of the option pricing problem lends itself very easily in using the ACO technique to the solution of computing option prices. ACO is as intuitive as other techniques such as binomial lattice approach. ACO searches the computational space eliminating areas that may not provide a profitable solution. The computational cost, therefore, tends to decrease during the execution of the algorithm. There has been no study reported in the literature on the use of ACO for pricing financial derivatives. We first study the suitability of ACO in finance and confirm that ACO could be applied to financial derivatives. We propose two ACO based algorithms to apply to derivative pricing problems in computational finance. The first algorithm, named Sub-optimal Path Generation is an exploitation technique. The second algorithm named the Dynamic Iterative Algorithm captures market conditions by using an exploration and exploitation technique. We analyze the advantages and disadvantages of both the algorithms. With both the algorithms we are able to compute the option values and we find that the sub-optimal path generation algorithm outperforms the binomial lattice method. The dynamic iterative algorithm can be used on any random graph and the uncertainties in the market can be captured easily but it is slower when compared to the sub-optimal path generation algorithm.