Option Pricing, Interest Rates and Risk Management by E. Jouini, J. Cvitanić, Marek Musiela

By E. Jouini, J. Cvitanić, Marek Musiela

This guide provides the present nation of perform, process and figuring out within the box of mathematical finance. every one bankruptcy, written by way of top researchers, begins by means of in brief surveying the prevailing effects for a given subject, then discusses more moderen effects and, eventually, issues out open issues of outlines for attainable strategies. the first audiences for the ebook are doctoral scholars, researchers and practitioners who have already got a few uncomplicated wisdom of mathematical finance. This accomplished reference paintings might be essential to readers who desire a quickly advent or references to precise issues inside this state-of-the-art fabric.

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And Pliska, S. (1981), Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications 11, 215–60. [24] Hubalek, F. and Schachermayer, W. (1998), When does convergence of asset price processes imply convergence of option prices? Mathematical Finance 8, 4, 215–33. [25] Huberman, G. (1982), A simple approach to arbitrage pricing theory. Journal of Economic Theory 28, 1, 183–91. , Jr. (1984), Some results in the theory of arbitrage pricing. Journal of Finance 39, 1021–39.

Thus, in the case of constant coefficients price processes are geometric Brownian motions as in the classical case of Black and Scholes. The model is designed to reflect the fact that in the market there are two different types of randomness: the first type is proper to each stock while the second one originates from some common source and it is accumulated in a “stock index” (or “market portfolio”) whose evolution is described by the first equation. Set γ σi γ σiσ0 β i := i = i 2 . σ0 σ0 In the case of deterministic coefficients, β i is a well-known measure of risk which is the covariance between the return on the asset with number i and the return on the index, divided by the variance of the return on the index.

M. Kabanov confirmed that such models are adequate tools to describe financial market phenomena. The current trend is to go beyond the Black–Scholes world. Statistical tests for financial data reject the hypothesis that prices evolve as processes with continuous sample paths. Much better approximation can be obtained by stable or other types of L´evy processes. Apparently, semimartingales provide a natural framework for discussion of general concepts of financial theory like arbitrage and hedging problems.

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