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657
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
Overconfidence and speculative bubbles
 Journal of Political Economy
, 2003
"... Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an ass ..."
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Cited by 329 (22 self)
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Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an asset owner has an option to sell the asset to other overconfident agents when they have more optimistic beliefs. As in Harrison and Kreps (1978), this resale option has a recursive structure, that is, a buyer of the asset gets the option to resell it. Agents pay prices that exceed their own valuation of future dividends because they believe that in the future they will find a buyer willing to pay even more. This causes a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. In equilibrium, large bubbles are accompanied by large trading volume and high price volatility. Our model has an explicit solution, which allows for several comparative statics exercises. Our analysis shows that while Tobin’s tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility. We also give an example where the price of a subsidiary is larger than its parent firm. This paper was previously circulated under the title “Overconfidence, ShortSale Constraints and Bubbles.”
Testing ContinuousTime Models of the Spot Interest Rate
 Review of Financial Studies
, 1996
"... Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are rec ..."
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Cited by 310 (9 self)
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Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then meanreverts strongly when far away from the mean. The volatility is higher when away from the mean. The continuoustime financial theory has developed extensive tools to price derivative securities when the underlying traded asset(s) or nontraded factor(s) follow stochastic differential equations [see Merton (1990) for examples]. However, as a practical matter, how to specify an appropriate stochastic differential equation is for the most part an unanswered question. For example, many different continuoustime The comments and suggestions of Kerry Back (the editor) and an anonymous referee were very helpful. I am also grateful to George Constantinides,
Optimal Prefetching via Data Compression
, 1995
"... Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the pr ..."
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Cited by 258 (7 self)
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Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to largescale databases and hypertext systems. Our prediction algorithms for prefetching are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, you have to be able to predict future data well, and thus good data compressors should be able to predict well for purposes of prefetching. We show for powerful models such as Markov sources and nth order Markov sources that the page fault rates incurred by our prefetching algorithms are optimal in the limit for almost all sequences of page requests.
Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model
, 1999
"... This paper presents a dynamic, rational expectations equilibrium model of asset prices where the drift of fundamentals (dividends) shifts between two unobservable states at random times. I show that in equilibrium, investors' willingness to hedge against changes in their own "uncertainty&q ..."
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Cited by 229 (9 self)
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This paper presents a dynamic, rational expectations equilibrium model of asset prices where the drift of fundamentals (dividends) shifts between two unobservable states at random times. I show that in equilibrium, investors' willingness to hedge against changes in their own "uncertainty" on the true state makes stock prices overreact to bad news in good times and underreact to good news in bad times. I then show that this model is better able than con ventional models with no regime shifts to explain features of stock returns, including volatility clustering, "leverage effects," excess volatility and timevarying expected returns.
Innovating Firms and Aggregate Innovation
, 2002
"... We develop a parsimonious model of innovating firms rich enough to confront firmlevel evidence. It captures the dynamic behavior of individual heterogenous firms, describes the evolution of an industry with simultaneous entry and exit, and delivers a general equilibrium model of technological chang ..."
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Cited by 220 (2 self)
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We develop a parsimonious model of innovating firms rich enough to confront firmlevel evidence. It captures the dynamic behavior of individual heterogenous firms, describes the evolution of an industry with simultaneous entry and exit, and delivers a general equilibrium model of technological change. While unifying the theoretical analysis of firms, industries, and the aggregate economy, the model yields insights into empirical work on innovating firms. It accounts for the persistence over time of firms ’ R&D investment, the concentration of R&D among incumbent firms, and the link between R&D and patenting. Furthermore, it explains why R&D as a fraction of revenues is strongly related to firm productivity yet largely unrelated to firm size or growth.
Corporate Investment and Asset Price Dynamics: Implications for the CrossSection of Returns
 Journal of Finance
, 2004
"... We show that corporate investment decisions can explain conditional dynamics in expected asset returns. Our approach is similar in spirit to Berk, Green, and Naik (1999), but we introduce to the investment problem operating leverage, reversible real options, fixed adjustment costs, and finite growth ..."
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Cited by 207 (8 self)
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We show that corporate investment decisions can explain conditional dynamics in expected asset returns. Our approach is similar in spirit to Berk, Green, and Naik (1999), but we introduce to the investment problem operating leverage, reversible real options, fixed adjustment costs, and finite growth opportunities. Asset betas vary over time with historical investment decisions and current product market demand. Booktomarket effects emerge and relate to operating leverage, while size captures the residual importance of growth options relative to assets in place. We estimate and test the model using simulation methods and reproduce portfolio excess returns comparable to the data. Corporate investment decisions are often evaluated in a real options context, 1 and option exercise can change the riskiness of a firm in various ways. For example, if growth opportunities are finite, the decision to invest changes the ratio of growth options to assets in place. Additionally, the resulting increase