Handbook of Computational and Numerical Methods in Finance

Mathematical finance has been an exponentially growing field of research in the last decades and is still impressively active. There are also many directions and subfields under the hat of 'finance' and researchers from very different fields, such as economics (of course), engineering, mathematics, numerical analysis and recently statistics, have been involved in this area.This chapter is intended to give a guidance on the reading of the book and to provide a better focus on the topics discussed herein. The book is intended to be self-contained in its exposition, introducing all the concepts, including very preliminary ones, which are required to better understand more complex topics and to appreciate the details and the beauty of some of the results.This book is also very computer-oriented and it often moves from theory to applications and examples. The R statistical environment has been chosen as a basis. All the code presented in this book is free and available as an R statistical package called opefimor on CRAN. 1 There are many good publications on mathematical finance on the market. Some of them consider only mathematical aspects of the matter at different level of complexity. Other books that mix theoretical results and software applications are usually based on copyright protected software. These publications touch upon the problem of model calibration only incidentally and in most cases the focus is on discrete time models mainly (ARCH, GARCH, etc.) with notable exceptions.The main topics of this book are the description of models for asset dynamics and interest rates along with their statistical calibration. In particular, the attention is on continuous time models observed at discrete times and calibration techniques for them in terms of statistical estimation. Then pricing of derivative contracts on a single underlining asset in the Black and Scholes-Merton framework (Black and Scholes 1973;Merton 1973), pricing of basket options, volatility, covariation and regime switching analysis are considered. At the same

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Construction of Quasi Optimal Portfolio for Stochastic Models of Financial Market

Janicki

Zwierz

2004

Computational Science - ICCS 2004

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Abstract. In the paper we propose a purely computational new method of construction of a quasi-optimal portfolio for stochastic models of a financial market. Here we present the method in the framework of a classical Black-Scholes model of a complete market (see, eg.[4], [6]), considering a well known optimal investment and consumption problem with the HARA type optimization functional. Our method is based on the idea to maximize this functional, taking into account only some subsets of possible portfolio and consumption processes. We show how to reduce the main problem to the construction of a portfolio maximizing a deterministic function of a few real valued parameters but under purely stochastic constraints. It is enough to solve several times an indicated system of stochastic differential equations (SDEs) with properly chosen parametrs. Results of computer experiments presented here were obtained with the use of the SDE-Solver software package. This is our own professional C++ application to Windows system, designed as a scientific computing tool based on Monte Carlo simulations and serving for numerical and statistical construction of solutions to a wide class of systems of SDEs, including a broad class of diffusions with jumps driven by non-Gaussian random measures (consultOur method can be easily extended to stochastic models of financial market described by systems of such SDEs. Optimal Investment and Consumption Problem for Black-Scholes Model of a Financial MarketLet us recall that an N dimensional Black-Scholes model of a financial market can be described by the following system of N + 1 SDEsS n (t) = S n (0) +

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Handbook of Computational and Numerical Methods in Finance

Abstract: Library of Congress Cataloging-in-Publication DataHandbook of computational and numerical methods in finance / Svetlozar T. Rachev, editor.p.cm. Includes bibliographical references.

Cited by 6 publications

References 78 publications

Option Pricing and Estimation of Financial Models with R

Option Pricing and Estimation of Financial Models with R

A Synthetic View

Construction of Quasi Optimal Portfolio for Stochastic Models of Financial Market

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