QUANTITATIVE FINANCE FOR PHYSICISTS: AN INTRODUCTION pot

[...]... computer science and mathematics majors who are willing to work (or have recently started a career) in the finance industry In addition, this book may be of interest to majors in economics and finance who are curious about Econophysics and agent-based modeling of financial markets This book can be used for self-education or in an elective course on Quantitative Finance for science and engineering majors... triangle foreign exchange arbitrage Consider a situation in which a trader can exchange one American dollar (USD) for one Euro (EUR) or for 120 Yen (JPY) In addition, a trader can exchange one EUR for 119 JPY Hence, in terms of the exchange rates, 1 USD/ JPY > 1 EUR/JPY * 1 USD/EUR.3 Obviously, the trader who operates, say 100000 USD, can make a profit by buying 12000000 JPY, then selling them for. .. the same currency and that the transportation and transaction costs can be neglected Violation of the Law of One Price leads to arbitrage, which means buying an asset and immediate selling it (usually in another market) with profit and without risk One widely publicized example of arbitrage is the notable differences in prices of prescription drugs in the USA, Europe, and Canada Another typical example... the statistical analysis of economic and financial time series [2] The other field is Mathematical Finance [3, 4] This term implies that finance has given a rise to several new mathematical theories The leading directions in Mathematical Finance include portfolio theory, option-pricing theory, and risk measurement The ‘‘academic’’ part of this book demonstrates that financial data can be an area of exciting... distribution with given uniform distribution [4] Namely, if two numbers x1 and x2 are drawn from the standard uniform distribution, then y1 and y2 are the standard normal variates y1 ¼ [À2 ln x1 )]1=2 cos (2px2 ), y2 ¼ [À2 ln x1 )]1=2 sin (2px2 ) (3:2:13) Mean and variance of the multivariate normal distribution with N variates can be easily calculated via the univariate means mi and covariances sij mN ¼ N X... Covariance between two variates provides a measure of their simultaneous change Consider two variates, X and Y, that have the means mX and mY , respectively Their covariance equals Cov(x, y)  sXY ¼ E[(x À mX )(y À mY )] ¼ E[xy] À mX mY (3:1:13) Obviously, covariance reduces to variance if X ¼ Y: sXX ¼ sX 2 Positive covariance between two variates implies that these variates tend to change simultaneously... with the covariance matrix Its elements equal Cov(xi , xj )  sij ¼ E[(xi À mi )(xj À mj )] (3:1:15) 3.2 IMPORTANT DISTRIBUTIONS There are several important probability distributions used in quantitative finance The uniform distribution has a constant value within the given interval [a, b] and equals zero outside this interval  0, x < a and x > b (3:2:1) PU ¼ 1=(b À a), a x b The uniform distribution... private (insider) information This implies that the fundamental analysis (which is what the investment analysts do) is not useful either The compromise between the strong and weak forms yields the ‘‘semistrong’’ form of EMH according to which prices reflect all publicly available information and the investment analysts play important role in defining fair prices Two notions are important for EMH The first... new outlook for the industry trend Macroeconomic and political events, or simply gossip about a company’s management, can also affect the stock price All these events imply that new information becomes available to markets The Efficient Market Theory states that financial markets are efficient because they instantly reflect all new relevant information in asset prices Efficient Market Hypothesis (EMH)... efficiency For example, an investor in an efficient market should not expect earnings above the market return while using technical analysis or fundamental analysis.4 Three forms of EMH are discerned in modern economic literature In the ‘‘weak’’ form of EMH, current prices reflect all information on past prices Then the technical analysis seems to be helpless In the ‘‘strong’’ form, prices instantly reflect . the accuracy and integrity of this document Date: 2005.06.16 05:44:41 +08'00' QUANTITATIVE FINANCE FOR PHYSICISTS: A N INTRODUCTION Schmidt / Quantitative Finance: An Introduction For Physicists. intentionally left blank QUANTITATIVE FINANCE FOR PHYSICISTS: A N INTRODUCTION ANATOLY B. SCHMIDT AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE. Econophysics and agent-based modeling of financial markets. This book can be used for self-education or in an elective course on Quantitative Finance for science and engineering majors. The book is organized