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622
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 1512 (6 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
Stock Returns and the Term Structure
 Journal of Financial Economics
, 1987
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. ..."
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Cited by 570 (26 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study.”
 Quarterly Journal of Economics
, 1997
"... ..."
On estimating the expected return on the market  an exploratory investigation
 JOURNAL OF FINANCIAL ECONOMICS
, 1980
"... The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market retu ..."
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Cited by 490 (3 self)
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The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive are derived and applied to return data for the period 19261978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return, the nonnegativity restriction of the expected excess return should be explicitly included as part of the specification; (2) estimators which use realized returns should be adjusted for heteroscedasticity.
and Spot Exchange Rates
 Journal qf Monetary Economics
, 1984
"... There is a general comemum that forward exchanse rates have tittle if any power as forecasts of future spot exchat ~ rateL There is less alpeentent on whether forward rates contain time varying premiumL Conditional on the bjpmlm ~ that the forward market is efficient or rational, this paper finds th ..."
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Cited by 444 (1 self)
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There is a general comemum that forward exchanse rates have tittle if any power as forecasts of future spot exchat ~ rateL There is less alpeentent on whether forward rates contain time varying premiumL Conditional on the bjpmlm ~ that the forward market is efficient or rational, this paper finds that both components of foewa ~ rates vary through time. Moreover. most of the variation in forward rates is variatioa in premiums, and the pr~mium and expected future spot rate components of forward rates are netatively correlat.,'d I. I n ~ There is much empirical work on forward foreign exchange rates as predictors of future spot exchange rates. [See, for exmnple, Hansen and Hodrick (1980)0 Bilson (1981), and the review article by Levich (1979).] There is also a growing literature on whethm " forward rates contain variation in premiums.
Efficient Capital Market: II” ,
 Journal of Finance, No
, 1991
"... SEQUELS ARE RARELY AS good as the originals, so I approach this review of the market efflciency literature with trepidation. The task is thornier than it was 20 years ago, when work on efficiency was rather new. The literature is now so large that a full review is impossible, and is not attempted h ..."
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Cited by 337 (0 self)
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SEQUELS ARE RARELY AS good as the originals, so I approach this review of the market efflciency literature with trepidation. The task is thornier than it was 20 years ago, when work on efficiency was rather new. The literature is now so large that a full review is impossible, and is not attempted here. Instead, I discuss the work that I find most interesting, and I offer my views on what we have learned from the research on market efficiency. I. The Theme I take the market efficiency hypothesis to be the simple statement that security prices fully reflect all available information. A precondition for this strong version of the hypothesis is that information and trading costs, the costs of getting prices to reflect information, are always 0 (Grossman and Stiglitz (1980)). A weaker and economically more sensible version of the efficiency hypothesis says that prices reflect information to the point where the marginal benefits of acting on information (the profits to be made) do not exceed the marginal costs (Jensen (1978)). Since there are surely positive information and trading costs, the extreme version of the market efficiency hypothesis is surely false. Its advantage, however, is that it is a clean benchmark that allows me to sidestep the messy problem of deciding what are reasonable information and trading costs. I can focus instead on the more interesting task of laying out the evidence on the adjustment of prices to various kinds of information. Each reader is then free to judge the scenarios where market efficiency is a good approximation (that is, deviations from the extreme version of the efficiency hypothesis are within information and trading costs) and those where some other model is a better simplifying view of the world. Ambiguity about information and trading costs is not, however, the main obstacle to inferences about market efficiency. The jointhypothesis problem is more serious. Thus, market efficiency per se is not testable. It must be
The CrossSection of Volatility and Expected Returns
 Journal of Finance
, 2006
"... We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF. ..."
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Cited by 267 (9 self)
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We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF.
Consumption strikes back? Measuring long run risk, working paper,
, 2005
"... Abstract We characterize and measure a longrun risk return tradeoff for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This tradeoff features the risk prices of cash flows that are realized far into the future but are reflected in asset values. We apply this analysis ..."
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Cited by 246 (32 self)
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Abstract We characterize and measure a longrun risk return tradeoff for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This tradeoff features the risk prices of cash flows that are realized far into the future but are reflected in asset values. We apply this analysis to a claims on aggregate cash flows, as well as to the cash flows from value and growth portfolios. Based on vector autoregressions, we characterize the dynamic response of cash flows to macroeconomic shocks and document that there are important differences in the longrun responses. We isolate those features of a recursive utility model and the consumption dynamics needed for the long run valuation differences among these portfolios to be sizable. Finally, we show how the resulting measurements vary when we alter the statistical specifications of cash flows and consumption growth.
Resurrecting the (C)CAPM: A CrossSectional Test When Risk Premia Are TimeVarying
 Journal of Political Economy
, 2001
"... This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditio ..."
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Cited by 246 (10 self)
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This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the FamaFrench threefactor model on portfolios sorted by size and booktomarket characteristics. The conditional consumption CAPM can account for the difference in returns between lowbooktomarket and highbooktomarket portfolios and exhibits little evidence of residual size or booktomarket effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the
Dynamic Nonmyopic Portfolio Behavior
 Review of Financial Studies
, 1996
"... The dynamic nonmyopic portfolio behavior of an investor who trades a riskfree and risky asset is derived for all HARA utility functions and a stochastic risk premium. Conditions are found for when the investor holds more or less than the myopic amount of the risky asset; hedges against or speculate ..."
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Cited by 190 (3 self)
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The dynamic nonmyopic portfolio behavior of an investor who trades a riskfree and risky asset is derived for all HARA utility functions and a stochastic risk premium. Conditions are found for when the investor holds more or less than the myopic amount of the risky asset; hedges against or speculates the riskpremium uncertainty; is long or short on the risky asset; and holds more or less of the risky asset at longer horizons. The analytical solutions derived take multiple mathematical forms and include extreme cases in which investors with long but finite horizons can attain nirvana. In the standard paradigm of portfolio theory, the investor maximizes expected utility, with continuous or periodic revisions of his portfolio within his investment horizon. The purpose of the revisions is to adapt to shifts in wealth, interest rates, and beliefs, and to the shortening of the investor’s horizon as time passes.1 The investor’s opportunity set is defined to be the current riskfree rate and his probability beliefs for The authors would like to thank David Feldman, Robert Merton, Paul Samuelson, editor Chifu Huang, executive editor Franklin Allen, and an anonymous reviewer for their comments and suggestions. Any errors are the responsibility of the authors. Address correspondence to Edward