Some Recent Developments in Capital Market Theory: A Survey

This paper surveys some recent developments in the theory of capital markets. Particular emphasis is given to two strands of the literature. The rst covers some recent and fundamental extensions to the theory of risk aversion and the demand for risky assets. These papers are concerned with the e ect of nonhedgeable background risk on risk attitudes. The important implications for nance are for the size of the risk premium (the equity premium puzzle) and for the demand for and pricing of contingent claims. For example, background risk may help to explain the apparent over-pricing of options on equity indices. The second topic is interest rate term structure models. Stochastic term structure models try to capture the possible future shapes of the term structure of interest rates. This is relevant for the pricing of contingent claims, in particular for the pricing of interest rate derivatives such as American-style swaptions. The paper will survey the most important recent models in the literature, each of which satis es the fundamental no-arbitrage property. It will discuss the implications of the models for the pricing of both European-style and American-style options. Capital market theory 1 1 Capital Market Theory: Introduction Capital market theory is about the pricing of assets, principally corporate assets. It holds a central place in the structure of nance theory. This is because nance studies the behaviour of corporations in issuing securities and investing in assets, and as a consequence studies the pricing of securities in capital markets. The cornerstones of capital market theory: the Capital Asset Pricing Model (CAPM), the Modigliani-Miller theorems (MM), and the Black-Scholes Option Pricing Model (OPM) were all in place twenty ve years ago. Before I begin to discuss more recent developments in the eld and current research activity, let me brie y outline these three paradigms and their relationship to each other. Consider a rm whose securities, stock and bonds, are traded on the stock market. Suppose, for example that the current total value of the rm is 1,000 million, made up of an equity stock market capitalisation of 700 million, and bonds with a value of 300 million. The role of asset pricing models in nance is to explain why the asset value of the rm is 1,000, given it's exogenously given expected cash ow. In particular, the CAPM attempts to explain the required expected rate of return on the rm's assets, given the beta of the rm. The MM theorems on the other hand tell us how the total value of the rm will be a ected if the rm recapitalised itself by issuing more debt and repaying some of its equity. Thirdly, since equity can be modelled as a call option on the rm's assets, the OPM can be used to explain why the equity of the rm is selling for 700 million given the volatility of the underlying assets. Of course, much work has been done extending the three basic paradigms over the last few years. Particular progress has been made in the area of option pricing and especially in the pricing of derivatives whose payo s depend on interest rates. The Black-Scholes model was initially applied to options on stocks, and then to options on foreign exchange and bonds. However, straightforward applications were found not to be appropriate in this latter case, since the assumptions of a constant volatility, lognormal process simply do not apply. At the same time the hedging of interest rate risk with options has become commonplace in practice. Hence a great deal of academic work has been undertaken, adapting the OPM to cope with the pricing of interest rate related contingent claims. In order to price more complex derivatives with path-dependent payo s, good models of the underlying term structure of interest rates are required. The most important developments in this area will be surveyed in the section 3 of this paper. The foundations of the CAPM are expected utility theory and the theory of state contingent pricing. The former is based on Von Neumann-Morgenstern utility, and the subsequent work of Pratt (1964) who de ned various concepts Capital market theory 2 of risk aversion and showed that, when faced with the choice of a risky and a riskless asset, more risk averse investors buy less of the risky asset. To an extent, the foundations of asset pricing have been broadened in recent years following the contribution of Harrison and Kreps (1979), who showed that a no-arbitrage economy implies the existence of an 'equivalent martingale measure' (EMM). The signi cance of the EMM lies in the fact that the price of any asset is the expectation of it's payo under the EMM. This has allowed many of the utlity based theories in nance to be generalised to a no-arbitrage economy. However, it is perhaps the case that this has led more to a change in the appearance of many papers in nance than to a signi cant change in content. Today we tend to speak of the pricing kernel whereas in the past we would have used the utility function of the representative investor. We will see this use of the EMM when we review interest rate models in section 3. I regard the border line between economics and nance in terms of the type of models employed as well as the subject matter. Economics tends to use equilibrium models whereas nance employs no-arbitrage techniques. The MM, OPM, and the APT (Arbitrage Pricing Theory) models, as well as much of the theory of International Finance, are prime examples of no-arbitrage theories. However, it should be remembered that these models are themselves embedded in some equilibrium economy. In most cases the propositions of nance rely on the fundamental work of economists. In this context it is interesting to note that some of the foundations of utility theory and risk-taking behaviour have been questioned by economists in recent work. The particular issue that I will emphasise in this survey is the e ect of secondary, non-hedgeable risks on investors' attitude to the risk of marketed assets. These non-hedgeable risks are often termed background risks, and typical among them is labor income risk. It appears that the existence of background risk can have profound implications for risk-taking, and for the pricing and use of nancial securities. The recent literature and its implications for nance theory is surveyed in section 2. Capital market theory 3 2 Background Risk and its Implications for Fi-