Perturbation Methods in Credit Derivatives

CHAPTER 1Why Perturbation Methods?

1.1 ANALYTIC PRICING OF DERIVATIVES

How important are analytic formulae in the pricing of financial derivatives? The way you feel about this matter will probably determine to a large degree whether this book will be of interest to you. Current opinion is undoubtedly divided and perhaps for good reasons. On the one hand, presented with the challenge of some new financial calculation, financial engineers these days are likely to spend considerably less time looking for analytic solutions or approximations than, say, twenty years ago, citing the ever‐increasing power and speed of computational resources at their disposal. On the other hand, where known analytic solutions exist, those same financial engineers are unlikely to eschew them and to persist doggedly in replicating the known solution using a Monte Carlo engine or a finite difference method.

So, it might be suggested, the resistance to analytic solutions that we observe is not to their use as such when they are already available, but to making the effort to find (and implement) them. One of the reasons for this is a perception that, given the huge amount of research effort that has been invested into finding solutions over the past few decades, most of the interesting and useful solutions have been found and published. It is the experience of the author that the reaction to the announcement of discovery of a new and interesting analytic solution tends to be indifference or scepticism ...