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AuthorBenth, Fred Espen. author
TitleOption Theory with Stochastic Analysis [electronic resource] : An Introduction to Mathematical Finance / by Fred Espen Benth
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
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Descript X, 162 p. 1 illus. online resource


The objective of this textbook is to provide a very basic and accessible introduction to option pricing, invoking only a minimum of stochastic analysis. Although short, it covers the theory essential to the statistical modeling of stocks, pricing of derivatives (general contingent claims) with martingale theory, and computational finance including both finite-difference and Monte Carlo methods. The reader is led to an understanding of the assumptions inherent in the Black & Scholes theory, of the main idea behind deriving prices and hedges, and of the use of numerical methods to compute prices for exotic contracts. Finally, incomplete markets are also discussed, with references to different practical/theoretical approaches to pricing problems in such markets. The author's style is compact and to-the-point, requiring of the reader only basic mathematical skills. In contrast to many books addressed to an audience with greater mathematical experience, it can appeal to many practitioners, e.g. in industry, looking for an introduction to this theory without too much detail. It dispenses with introductory chapters summarising the theory of stochastic analysis and processes, leading the reader instead through the stochastic calculus needed to perform the basic derivations and understand the basic tools It focuses on ideas and methods rather than full rigour, while remaining mathematically correct. The text aims at describing the basic assumptions (empirical finance) behind option theory, something that is very useful for those wanting actually to apply this. Further, it includes a big section on pricing using both the pde-approach and the martingale approach (stochastic finance). Finally, the reader is presented the two main approaches for numerical computation of option prices (computational finance). In this chapter, Visual Basic code is supplied for all methods, in the form of an add-in for Excel. The book can be used at an introductory level in Universities. Exercises (with solutions) are added after each chapter


1 Introduction -- 1.1 An Introduction to Options in Finance -- 1.2 Some Useful Material from Probability Theory -- 2 Statistical Analysis of Data from the Stock Market -- 2.1 The Black & Scholes Model -- 2.2 Logarithmic Returns from Stocks -- 2.3 Scaling Towards Normality -- 2.4 Heavy-Tailed and Skewed Logreturns -- 2.5 Logreturns and the Normal Inverse Gaussian Distribution -- 2.6 An Alternative to the Black & Scholes Model -- 2.7 Logreturns and Autocorrelation -- 2.8 Conclusions Regarding the Choice of Stock Price Model -- 3 An Introduction to Stochastic Analysis -- 3.1 The Itรด Integral -- 3.2 The Itรด Formula -- 3.3 Geometric Brownian Motion as the Solution of a Stochastic Differential Equation -- 3.4 Conditional Expectation and Martingales -- 4 Pricing and Hedging of Contingent Claims -- 4.1 Motivation from One-Period Markets -- 4.2 The Black & Scholes Market and Arbitrage -- 4.3 Pricing and Hedging of Contingent Claims X= f(S(T)) -- 4.4 The Girsanov Theorem and Equivalent Martingale Measures -- 4.5 Pricing and Hedging of General Contingent Claims -- 4.6 The Markov Property and Pricing of General Contingent Claims -- 4.7 Contingent Claims on Many Underlying Stocks -- 4.8 Completeness, Arbitrage and Equivalent Martingale Measures -- 4.9 Extensions to Incomplete Markets -- 5 Numerical Pricing and Hedging of Contingent Claims -- 5.1 Pricing and Hedging with Monte Carlo Methods -- 5.2 Pricing and Hedging with the Finite Difference Method -- A Solutions to Selected Exercises -- References

Finance Economics Mathematical Probabilities Statistics Finance Finance general Probability Theory and Stochastic Processes Quantitative Finance Statistics for Business/Economics/Mathematical Finance/Insurance


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