Continuous-Time Finance (Macroeconomics and Finance)
By Robert C. Merton
* Publisher: Wiley-Blackwell
* Number Of Pages: 752
* Publication Date: 1992-11-10
* ISBN-10 / ASIN: 0631185089
* ISBN-13 / EAN: 9780631185086
Product Description:
Robert C. Merton's widely used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual financial choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance. For this revised edition a new section on managing university endowments has been added. The book begins with a foreword by Paul Samuelson.
Summary: Excellent presentation of Financial theory application IF the central limit theorem holds
Rating: 5
Merton's book presents the continuous time generalization of existing finance theory.A good representative section ,demonstrating his technique throughout the book,is contained in his generalization of the Tobin-Markowitz mean -variance approach using the log normal distribution to artificilly minimize the presence of outliers(pp.131-136).Throughout the book Merton uses the word " uncertainty " when he should be using the word " risk ".The entire book is based on the assumption that the central limit theorem holds so that one does not need to consider any other possible distribution shape except the normal because the distribution of the sample means will always be normally distributed for large samples taken from any other shaped distribution.However,this requires that the sample space be composed entirely of continuous and independent observations.The purpose of goodness of fit tests is to establish that the assumptions of the central limit theorem do,in fact ,hold.Nowhere in this book is a single goodness of fit test mentioned or reported.In fact,there is no discussion of any of the existing types of goodness of fit tests at all.Benoit Mandelbrot has demonstrated for about 50 years that the time series data on price changes in financial markets world wide is NOT continuous(they are discrete , bunched,and change in data jumps )and NOT independent(they are dependent-moreover, the time sequence of the events is extremely important).Mandelbrot's critique is thus a much more advanced form of the initial objections raised by J M Keynes to Jan Tinbergen's 1937-38 use of least squares to predict changes in investment spending over time, based primarily on Tinbergen's use of a lagged expectations variable,that appeared in the Economic Journal of 1939-40.Keynes asked Tinbergen to show that his time series data was "...uniform,stable,and homogeneous through time." Tinbergen never demonstrated this at any time in his life .How does Merton deal with the fact that the normal distribution does not come close to approximating the time series data in financial markets ? His response is to cite Paul Cootner's reply made to Mandelbrot in 1963 : " Moreover,as discussed by Cootner...the infinite variance property of the non-Gaussian stable distributions implies that most(all? -author's insert) of our statistical tools ,which are based upon finite moment assumptions(e.g.least squares),are useless.It also implies that even the first moment ,or expected value of the arithmetic price change,does not exist."(p.59).Merton concedes that the L(Levy) stable distributions Mandelbrot has studied fit the actual tail values of the time series data better than the Gaussian does.
The conclusion that I have arrived at in this review is that Merton's techniques are valuable IF the data is continuous,independent,and path independent.On the other hand,Mandelbrot's approach is to be preferred if the time series data is discontinuous,dependent,and path dependent.Merton's approach implies that the private financial markets of the world are stable and convergent over time to a rational expectations equilibrium.The decision maker faces " mild " risk that can be insured against by the holding of various options and derivatives.Mandelbrot's approach implies that the world's private financial markets are unstable and do not converge to a rational expectations equilibrium.The decision maker faces " wild " risk that can't be insured against.
http://ifile.it/sf0zpbd/continuous-time_finance__merton_.pdf
