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好东西 Introduction Financial economics plays a far more prominent role in the training of economists than it did even a few years ago.This change is generally attributed to the parallel transformation in capital markets that hasoccurred in recent years. It is true that trillions of dollars of assets are traded daily in ¯nancial markets|for derivative securities like options and futures, for example|that hardly existed a decade ago. However, it is less obvious how important these changes are. Insofar as derivative securities can be valued by arbitrage, such securities only duplicate primary securities. For example,to the extent that the assumptions underlying the Black-Scholes model of option pricing (or any of its more recent extensions) are accurate, the entire options market is redundant, since by assumption the payo® of an option can be duplicated using stocks and bonds. The same argument applies to other derivative securities markets. Thus it is arguable that the variables that matter most| consumption allocations|are not greatly a®ected by the change in capital markets. Along these lines one would no more infer the importance of ¯nancial markets from their volume of trade than one would make a similar argument for supermarket clerks or bank tellers based on the fact that they handle large quantities of cash. In questioning the appropriateness of correlating the expanding role of ¯nance theory to the explosion in derivatives trading we are in the same position as the physicist who demurs when journalists express the opinion that Einstein's theories are important because they led to the devel-opment of television. Similarly, in his appraisal of John Nash's contributions to economic theory,Myerson [13] protested the tendency of journalists to point to the FCC bandwidth auctions as indicating the importance of Nash's work. At least to those with some curiosity about the physical and social sciences, Einstein's and Nash's work has a deeper importance than television and the FCC auctions! The same is true of ¯nance theory: its increasing prominence has little to do with the expansion of derivatives markets, which in any case owes more to developments in telecommunications and computing than in ¯nance theory. A more plausible explanation for the expanded role of ¯nancial economics points to the rapid development of the ¯eld itself. A generation ago ¯nance theory was little more than institutional description combined with practitioner-generated rules of thumb that had little analytical basis and, for that matter, little validity. Financial economists agreed that in principle security prices ought to be amenable to analysis using serious economic theory, but in practice most did not devote much e®ort to specializing economics in this direction. Today, in contrast, ¯nancial economics is increasingly occupying center stage in the economic analysis of problems that involve time and uncertainty. Many of the problems formerly analyzed using methods having little ¯nance content now are seen as ¯nance topics. The term structure of interest rates is a good example: formerly this was a topic in monetary economics; now it is a topic in ¯nance. There can be little doubt that the quality of the analysis has improved immensely as a result of this change. Increasingly ¯nance methods are used to analyze problems beyond those involving securities prices or portfolio selection, particularly when these involve both time and uncertainty. An example is the \real options" literature, in which ¯nance tools initially developed for the analysis of option markets are applied to areas like environmental economics. Such areas do not deal with options per se, but do involve problems to which the idea of an option is very much relevant. Financial economics lies at the intersection of ¯nance and economics. The two disciplines are di®erent culturally, more so than one would expect given their substantive similarity. Partly this re°ects the fact that ¯nance departments are in business schools and are oriented towards ¯nance practitioners, whereas economics departments typically are in liberal arts divisions of colleges and universities, and are not usually oriented toward any single nonacademic community.From the perspective of economists starting out in ¯nance, the most important di®erence is that ¯nance scholars typically use continuous-time models, whereas economists use discrete time models. Students do not fail to notice that continuous-time ¯nance is much more di±cult mathematically than discrete-time ¯nance, leading them to ask why ¯nance scholars prefer it. The question is seldom discussed. Certainly product di®erentiation is part of the explanation, and the possibility that entry deterrence plays a role cannot be dismissed. However, for the most part the preference of ¯nance scholars for continuous-time methods is based on the fact that the problems that are most distinctively those of ¯nance rather than economics|valuation of derivative securities, for example|are best handled using continuous-time methods. The reason is technical: it has to do with the e®ect of risk aversion on equilibrium security prices in models of ¯nancial markets.In many settings risk aversion is most conveniently handled by imposing a certain distortion on the probability measure used to value payo®s. It happens that (under very weak restrictions) in continuous time the distortion a®ects the drifts of the stochastic processes characterizing the evolution of security prices, but not their volatilities (Girsanov's Theorem). This is evident in the derivation of the Black-Scholes option pricing formula. In contrast, it is easy to show using examples that in discrete-time models distorting the un- derlying measure a®ects volatilities as well as drifts. As one would expect given that the e®ect disappears in continuous time, the e®ect in discrete time is second-order in the time interval. The presence of these higher-order terms often makes the discrete-time versions of valuation problems intractable. It is far easier to perform the underlying analysis in continuous time, even when one must ultimately discretize the resulting partial di®erential equations in order to obtain numerical solutions. For serious students of ¯nance, the conclusion from this is that there is no escape from learning continuous-time methods, however di±cult they may be. Despite this, it is true that the appropriate place to begin is with discrete-time and discrete- state models|the maintained framework in this book|where the economic ideas can be discussed in a setting that requires mathematical methods that are standard in economic theory. For most of this book (Parts I - VI) we assume that there is one time interval (two dates) and a single consumption good. This setting is most suitable for the study of the relation between risk and return on securities and the role of securities in allocation of risk. In the rest (Parts VII - VIII), we assume that there are multiple dates (a ¯nite number). The multidate model allows for gradual resolution of uncertainty and retrading of securities as new information becomes available.

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