New PDF release: Quantitative Methods in Derivatives Pricing: An Introduction

By Domingo Tavella

ISBN-10: 0471394475

ISBN-13: 9780471394471

This e-book turns out to were written for mathematical finance experts...but then what is the aspect? should you already comprehend the stuff, why trouble deciding to buy a booklet you realize every little thing approximately?

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Additional resources for Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance

Example text

The reader interested in more detailed information on probability measures is referred to the excellent book by Billingsley (1994). 12 QUANTITATIVE METHODS IN DERIVATIVES PRICING RANDOM VARIABLES A random variable is a function that maps the elements of ⍀ to the set of real numbers. For the same sample space, we can have different random variables. In our example, the stock price at an observation time is a random variable. The number of times the stock price exceeds a given amount is another random variable.

8) where we adopt a simple notation for the conditional expectation operator. Y is an Ft-measurable random variable. 10) We will typically be referring to conditional expectations when the ␴algebras are elements of a filtration F. 11) Martingales Assume that St is a stochastic process adapted to Ft , 0 £ t £ T. 12) WIENER PROCESS The Wiener process, also known as Brownian motion, is the basic process of continuous-time financial modeling. To visualize a Wiener process, consider a sequence of up and down moves of the price process, St.

14) For simplicity, we omit reference to the sample point ␻, and use subscripts for the time dependence. A Wiener process is adapted to a ␴-algebra Ft . The filtration { F t } t ‡ 0 can be the one generated by the Wiener process itself, or it can be one generated by the Wiener process as well as other processes, as long as the other processes don’t reveal information about future movements of the Wiener process. The following are additional properties of the Wiener process: ■ The Wiener process is Markovian.

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Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance by Domingo Tavella

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