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The Full Monte -- nearly
From
RISK Magazine
, March 1999
By Rich Tanenbaum, Guest Reviewer
Monte Carlo: Methodologies and Applications for Pricing and Risk Management,
Risk Publications
This book strives to describe Monte Carlo in full, including every procedure needed to implement state-of-the-art simulation techniques.
It is an ambitious goal, and the book largely succeeds, by means of original research papers and chapters written by authors re-explaining in plain English concepts that others have uncovered. But some of the chapters’ conclusions are contradictory, with one set of authors claiming deterministic methods do not work well for problems with many time periods, and others asserting that deterministic methods are far superior. Unfortunately, no one agrees on which securities will react favourably to which methods.
The book covers the use of Monte Carlo for pricing, approaches for valuing American-style options, VAR and several deterministic methods for carrying out Monte Carlo. It rises above the ubiquitous finance handbooks because it generally provides enough information for readers to reproduce the ideas presented.
But while the authors incorporate deriving asset prices, more time should have been devoted to the generation of option Greeks, which are extremely important (we can observe bids and offers, but we need price sensitivities to manage a deal). And every chapter on speeding up calculations uses convergence of price as the determinant of efficiency, without noting how good the new method is at accelerating the estimation of sensitivities.
The book explores various tricks for obtaining sound results with ever fewer simulations. These involve two types of techniques: control variates and the use of "good" random numbers.
Control variates simulate two assets using the same random numbers: the option in question (A) and a similar asset (B) whose value we know from a formula (B’). The final value is A+B’ - B. The notion of using "good" random numbers (called deterministic methods, since the numbers are no longer random) covers techniques that all boil down to the same concept: evenly dispersed random numbers give better results than random numbers that cluster in some spots, and miss other spots completely. In short, control variates adjust the output, and deterministic methods adjust the inputs. The good news is that these two methodologies are not mutually exclusive.
On the whole, Dupire has done a fine job of organising a random set of papers on Monte Carlo into a logical framework. He has also written excellent introductions to each section summarising the papers clearly. This makes the book almost as much fun as visiting the casino.
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