Financial Modelling with Jump Processes

Rating:
Summary: Impressive book with a hiccup
Review: A book dealing comprehensively with discontinuous asset prices has long been overdue. This is a first attempt to fill the gap in a manner both rigorous and accessible. The reason why it has taken so long for a book of this kind to appear is that price jumps give rise to a host of issues that are simply not present in continuous models such as Black-Scholes. The authors tackle most of them admirably. The book also contains valuable comprehensive bibliography.

Every pioneer can make a mistake. The authors do not shy away from very complicated questions, such as (locally) optimal hedging in the presence of jumps. I'm afraid they haven't done their homework properly in this case. They claim on page 339 "the minimal martingale measure preserves orthogonality", which happens to be true for continuous price processes but it is false in most models with jumps. Pages 340 and 341 go on to compute the locally risk minimizing hedging coefficients based on the false premise. I hope this can be fixed in the next edition.


Rating:
Summary: Too much focus on the mathematics
Review: I miss the step to practice and would like to see these mathematical formulas work. For me it contained too much (unuseful) mathematics and proofs. Good maybe for mathematicians, but for banking people on the edge of being unreadable. It is very time consuming to browse more then 500 pages and then still to have to work out all details to implement things. Also the stochastic volatily models are too briefly covered.