Genetic algorithms for tree based calibration problems
Loizos Andrea Talias · Spiral (Imperial College London) · 2005
Calibration is one of the most important issues faced on a trading floor nowdays.The objective of the thesis is to develop a genetic algorithm to deal with the problem of calibrating the binomial tree.We show that conventional genetic algorithms fails to capture the combinatorial nature of the tree and we introduce the so-called subgraph operator which preserves the risk-neutral forward conditions in the trees.We show that the simplest genetic algorithm is unable to perform any search of the solution space and that the combinatorial nature of the tree is difficult to be exploited during the simulation process.A variety of objective functions are used and the results show that the logarithmic error difference function is the most suitable objective function in the case of the problem of calibrating the binomial tree.An alternative algorithm called the bionomic algorithm is introduced which is shown to perform relatively-well.The algorithm is based on the iterative improvement of an initial feasible population set, with high quality solutions given more trials in the recombining step.The results show that the bionomic algorithm outperforms the results produced by the genetic algorithm.Results are presented for the calibration of non-recombining binomial trees of up to seven time-steps.The binomial trees are calibrated to a set of European style call and put options of various striking prices and the same time to maturity.