Financial Modelling with Jump Processes (Chapman & Hall/CRC Financial Mathematics Series)
Peter Tankov | 2003-12-30 00:00:00 | Chapman and Hall/CRC | 552 | Finance
During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Lévy processes are beyond their reach.Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by its use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations. Topics covered in this book include: jump-diffusion models, Lévy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.
Reviews
This book is an approach to economics in according to a very strong mathematical structure.
It is simply to explicate the concept why Tankov apply the Lévy processes.
The Black-Scholes theory is failed and we use the existence of jump to approximate better the financial phenomena.
Reviews
There is JUST the right amount of mathematics! Around every mathematical expression, there is a long discussion to explain what's going on. This is the best book there is on applications of Levy processes to finance, no question about it ...
Reviews
The authors not only understand the math, but also integrate the math with financial economics well. I think Levy process is the way to go in the next decade. For example, fundamentally speaking, Brownian motion cannot explain the equity premium puzzle, hence people resort to other factors, such as incomplete market, behaviors, prospect theory, etc. However, behavioral explanations cannot stand in the long run. Prospect theory may reveal what a "normal" person usually do, but once it is revealed, a normal person can get "smarter" and overcome his/her impetus in making suboptimal decisions. Then behavioral andirrational explanation will fail (eventually). One thing I found from my own research is that the Levy process may be an important yet often ignored factor that can explain unexplained issues in finance, hence we do not have to reply on shaky behavioral and irrational arguments. One last point, behavioral can be either rational (good, correct and acceptable) or irrational (bad and should be got rid of. This would be the long long journey for a person who has deep beliefs in science).
Reviews
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.
Reviews
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.
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