However my chief complaint is with the way the (very interesting and important) contect is presented -- Shaw simply contents himself with showing pages and pages of mathematica code, which is ugly and annoying to read. He doesn't even use indentations or keyword-highlighting to make the Mathematica code easier to read. What an unbelievable four-letter-word mess! Many mathematical concepts are buried within Mathematica code. A much better book would have resulted if he sat down and presented math as math rather than as Mathematica code. Very disappointing work from a writer who clearly seems to have an in-depth knowledge of finite difference methods.

1. The Parkville, Aus reader seems to be confused about the use of Monte Carlo simulation. The MC methods use LOG-normal methods, not Normal. Note that one can use several methods for simulating paths of asset prices. I have highlighted 3 approaches (i) fine clockwork paths, (ii) coarse clockwork paths, (iii) "events" or arbitrary time intervals (pp 407-411). Choice (i) should NOT be used for large time intervals or large volatility, as method (i) is based on the differential, and hence, for finite time intervals, approximate, form of the random walk, whereas (ii) and (iii) use the accurate integrated form, and will never give negative asset prices. In fact the book is generally rather clear on the need to avoid negative asset prices, and, in the case of tree models, carefully avoids either negative asset prices or probabilities, unlike most other texts!

2. MrBoonstra made an interesting comment about Mathematica vs C++ vs Java. I think many organizations waste a fortune replicating basic Mathematica functions in C++ or Java, either with expensive libraries, or worse still, re-writing them themselves only to see the programmers who wrote them move on! If you need to distribute these models the answer is to use a server with a number of Excel-linked clients, or nowadays, JLink - the Java link kit.