Titlebook: Martingale Methods in Financial Modelling; Marek Musiela,Marek Rutkowski Book 19971st edition Springer-Verlag Berlin Heidelberg 1997 Arbit

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The Black-Scholes Modelt is computationally simple and, like all arbitrage-based pricing models, does not require the knowledge of an investor’s risk preferences. Option valuation within the Black-Scholes framework is based on the already familiar concept of perfect replication of contingent claims. More specifically, we

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Modifications of the Black-Scholes Modelostponed to Chap. 10, however). The first section deals with the Black model of futures prices, in particular, the classic Black futures formula is derived. Subsequently, the standard Black-Scholes valuation result is extended to the case of an option written on a dividend-paying stock. The last sec

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Foreign Market Derivativesfree bonds and foreign stocks (and their derivatives), is allowed. We will work within the classic Black-Scholes framework. More specifically, both domestic and foreign risk-free interest rates are assumed throughout to be nonnegative constants, and the foreign stock price and the exchange rate are

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Continuous-time Security Marketss based on the notion of the It? stochastic integral with respect to a semi-martingale. Such a model of financial market, in which the arbitrage-free property hinges on the chosen class of admissible trading strategies, is termed the . hereafter. The relevance of a judicious choice of a numeraire pr

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Interest Rates and Related Contractsrld practice, several fixed-income markets operate; as a result, many concepts of interest rates have been developed. There is no doubt that management of interest rate risk, by which we mean the control of changes in value of a stream of future cash flows resulting from changes in interest rates, o

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Models of the Short-term Rateuous-time framework; a detailed presentation of a discrete-time approach to term structure modelling is done in Jarrow (1996). We start this chapter by addressing the existence and uniqueness of an arbitrage-free family of bond prices related to a given short-term rate process. To obtain more explic

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