Computational finance

Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a freeboundary partial differential equation.
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It was in late 1995 to early 1996 (shortly after the birth of his first daughter Claire) that the author first began to read the currently available finance books in order to write C/Cþþ financial software. However, apart fromthe book Options Futures and Other Derivatives by John Hull, he found very little information of practical help and had to trawl through the original journal articles in the Bodleian library for more information. Even then much information on how to implement and test various models was not included.
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In a beauty contest for companies, the winner is . . . General Electric. Or at least General Electric is the most admired company in America, according to Fortunemagazine’s annual survey. The other top ten ﬁnalists are Cisco Systems,Wal Mart Stores, Southwest Airlines, Microsoft, Home Depot, Berkshire Hathaway, Charles Schwab, Intel, and Dell Computer.What do these companies have that separates them from the rest of the pack?
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A First Course in Discrete Mathematics I. Anderson Analytic Methods for Partial Differential Equations G. Evans, J. Blackledge, P. Yardley Applied Geometry for Computer Graphics and CAD D. Marsh Basic Linear Algebra, Second Edition T.S. Blyth and E.F. Robertson Basic Stochastic Processes Z. Brze´ niak and T. Zastawniak z Elementary Differential Geometry A. Pressley Elementary Number Theory G.A. Jones and J.M. Jones Elements of Abstract Analysis M. Ó Searcóid Elements of Logic via Numbers and Sets D.L. Johnson...
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This book reports initial efforts in providing some useful extensions in financial modeling; further work is necessary to complete the research agenda. The demonstrated extensions in this book in the computation and modeling of optimal control in finance have shown the need and potential for further areas of study in financial modeling. Potentials are in both the mathematical structure and computational aspects of dynamic optimization. There are needs for more organized and coordinated computational approaches.
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This book is designed for students and researchers who want to develop professional skill in modern quantitative applications in nance. The Center for Applied Statistics and Economics (CASE) course at HumboldtUniversitat zu Berlin that forms the basis for this book is oered to interested students who have had some experience with probability, statistics and software applications but have not had advanced courses in mathematical nance.
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This chapter deals with the most basic concepts in finance: future value, present value, and internal rate of return. These concepts tell you how much your money will grow if deposited in a bank (future value), how much promised future payments are worth today (present value), and what percentage rate of return you’re getting on your investments (internal rate of return).
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Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief, in constructing and exploiting natural differentiable structures on abstract probability spaces; in other words, Stochastic Calculus of Variations proceeds from a merging of differential calculus and probability theory. As optimization under a random environment is at the heart of mathematical finance, and as differential calculus is of paramount importance for the search of extrema, it is not surprising that Stochastic Calculus of Variations appears in mathematical finance.
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To fulfill the promise of systems integration, a wide range of component technologies—including databases, operating systems, architectures, networks, security mechanisms, human interfaces, artificial intelligence, and communications—must work together. Expertise about the many domains in which systems integration is applied (finance, retail, transportation, and so on) must also be invoked. Thus an interdisciplinary approach is essential
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Learning objectives of this chapter include: How to apply the percentage of sales method, how to compute the external financing needed to fund a firm’s growth, the determinants of a firm’s growth, some of the problems in planning for growth.
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After studying this chapter, you should understand: How to standardize fi nancial statements for comparison purposes; how to compute and, more importantly, interpret some common ratios; the determinants of a fi rm’s profi tability; some of the problems and pitfalls in fi nancial statement analysis.
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After studying this chapter in the lecture, you should be able to: Explain how financial leverage affects earnings per share (EPS) and return on equity (ROE), compute the degree of financial leverage, define and compute the indifference earnings before interest and taxes (EBIT) and explain its importance in selecting between alternative financing opportunities, define and explain the term homemade leverage, explain why determining the optimal capital structure is important,...
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After studying chapter 25 in the lecture, you should be able to: Give the definitions for a put option and a call option, be familiar with common stock option quotations, illustrate the payoffs from a put and call option at maturity, explain how to determine the upper and lower bounds on a call option's value, compute the value of a call option based on the assumption that it is certain that the option will finish in the money,...
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This paper addresses the problem of developing a large semantic lexicon for natural language processing. The increas~g availability of machine readable documents offers an opportunity to the field of lexieal semantics, by providing experimental evidence of word uses (online texts) and word definitions (online dictionaries). The system presented hereafter, PETRARCA, detects word e.occurrences from a large sample of press agency releases on finance and economics, and uses these associations to build a easebased semantic lexicon. ...
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Chapter 13  Working with financial statements. In this chapter, you will know how to standardise financial statements for comparison purposes, know how to compute and interpret important financial ratios, know the determinants of a firm’s profitability and growth, understand the problems and pitfalls in financial statement analysis.
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Chapter 4 introduction to valuation: The time value of money. After completing this unit, you should be able to compute the future value of an investment made today, be able to compute the present value of cash to be received at some future date, be able to compute the return on an investment.
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In this chapter, students will be able to understand: Be able to compute the future value of multiple cash flows, be able to compute the present value of multiple cash flows, be able to compute loan payments, be able to find the interest rate on a loan, understand how loans are amortised or paid off, understand how interest rates are quoted.
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The topics discussed in this chapter are equity markets and stock valuation. After completing this unit, you should be able to: Understand how share prices depend on future dividends and dividend growth, be able to compute share prices using the dividend growth model, understand how share markets work, understand how share prices are quoted.
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Chapter 16 introduces you to shortterm financial planning. After completing this unit, you should be able to: Be able to compute the operating and cash cycles and understand why they are important, understand the different types of shortterm financial policy, understand the essentials of shortterm financial planning.
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Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "realworld" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.
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