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21
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 188 (13 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.”
Alternative characterizations of American put options
 Mathematical Finance
, 1992
"... Viswanathan, and the participants of workshops at Vanderbilt University and Cornell University. The first two authors are grateful for financial support from Banker’s Trust. We are particularly grateful to Henry McKean for many valuable discussions. Alternative Characterizations of American Put Opti ..."
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Cited by 56 (2 self)
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Viswanathan, and the participants of workshops at Vanderbilt University and Cornell University. The first two authors are grateful for financial support from Banker’s Trust. We are particularly grateful to Henry McKean for many valuable discussions. Alternative Characterizations of American Put Options We derive alternative representations of the McKean equation for the value of the American put option. Our main result decomposes the value of an American put option into the corresponding European put price and the early exercise premium. We then represent the European put price in a new manner. This representation allows us to alternatively decompose the price of an American put option into its intrinsic value and time value, and to demonstrate the equivalence of our results to the McKean equation. Alternative Characterizations of American Put Options The problem of valuing American options continues to intrigue finance theorists. For example, in
Pathwise Inequalities for Local Time: Applications to Skorokhod Embeddings and Optimal Stopping. Annals of Applied Probability
, 2008
"... We develop a class of pathwise inequalities of the form H(Bt) ≥ Mt + F(Lt), whereBt is Brownian motion, Lt its local time at zero and Mt alocal martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to d ..."
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Cited by 11 (1 self)
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We develop a class of pathwise inequalities of the form H(Bt) ≥ Mt + F(Lt), whereBt is Brownian motion, Lt its local time at zero and Mt alocal martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to derive constructions and optimality results of Vallois ’ Skorokhod embeddings. We discuss their financial interpretation in the context of robust pricing and hedging of options written on the local time. In the final part of the paper we use the inequalities to solve a class of optimal stopping problems of the form sup τ E[F(Lτ) − ∫ τ 0 β(Bs)ds]. The solution is given via a minimal solution to a system of differential equations and thus resembles the maximality principle described by Peskir. Throughout, the emphasis is placed on the novelty and simplicity of the techniques. 1. Introduction. The
Large Traders, Hidden Arbitrage and Complete Markets
 Journal of Banking and Finance
, 2005
"... This paper studies hidden arbitrage opportunities in markets where large traders affect the price process, and where the market is complete (in the classical sense). The arbitrage opportunities are “hidden” because they occur on a small set of times (typically of Lebesgue measure zero). These arbitr ..."
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Cited by 5 (1 self)
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This paper studies hidden arbitrage opportunities in markets where large traders affect the price process, and where the market is complete (in the classical sense). The arbitrage opportunities are “hidden” because they occur on a small set of times (typically of Lebesgue measure zero). These arbitrage opportunities occur naturally in markets where a large trader supports the price of some asset or commodity, for example corporate stock repurchase plans, government interest rate or foreign currency intervention, and price support by investment banks in IPOs. We also illustrate immediate arbitrage opportunities generated by usual market activity at specific points in time, for example the issuance date of an IPO or the inclusion date of a new stock in the S&P 500 index. 1
Put Call Reversal
, 2002
"... Assuming that the stock price process is a jump diffusion, we derive a new relation between puts and calls termed Put Call Reversal (PCR). We show how PCR gives simple new probabilistic interpretations of deltas and gammas. We also show how PCR simplifies semistatic hedging of long dated options. ..."
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Cited by 5 (3 self)
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Assuming that the stock price process is a jump diffusion, we derive a new relation between puts and calls termed Put Call Reversal (PCR). We show how PCR gives simple new probabilistic interpretations of deltas and gammas. We also show how PCR simplifies semistatic hedging of long dated options.
Overconfidence, ShortSale Constraints, and Bubbles
 JOURNAL OF POLITICAL ECONOMY
, 2001
"... Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to othe ..."
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Cited by 5 (0 self)
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Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to other agents when they have more optimistic beliefs. This resale option has a recursive structure, that is a buyer of the asset gets the option to resell it, causing a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. The model generates prices that are above fundamentals, excessive trading, and excess volatility. We also give an example where the price of a subsidiary is larger than its parent firm. 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.
Spatial analysis of time series
 FEMES Meetings
, 2006
"... In this paper, we propose a method of analyzing time series, called the spatial analysis. The analysis consists mainly of the statistical inference on the distribution given by the expected local time, which we define to be the spatial distribution, of a given time series. The spatial distribution i ..."
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Cited by 4 (0 self)
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In this paper, we propose a method of analyzing time series, called the spatial analysis. The analysis consists mainly of the statistical inference on the distribution given by the expected local time, which we define to be the spatial distribution, of a given time series. The spatial distribution is introduced primarily for the analysis of nonstationary time series whose distributions change over time. However, it is well defined for both stationary and nonstationary time series, and reduces to the time invariant stationary distribution if the underlying time series is indeed stationary. The spatial analysis may therefore be regarded as an extension of the usual inference on the distribution of a stationary time series to accommodate for nonstationary time series. In fact, we show that the concept of the spatial distribution allows us to extend many notions and ideas built upon the presumption of stationarity and make them applicable also for the analysis of nonstationary data. Our approach is nonparametric, and imposes very mild conditions on the underlying time series. In particular, we allow for the observations generated from a wide class of stochastic processes with stationary and mixing increments, or general markov processes including virtually all diffusion models used in practice. For illustration, we provide some empirical applications of our methodology to various topics such as the risk management, distributional dominance and option pricing.
Local time and the pricing of timedependent barrier options
 Accepted in Finance and Stochastics
, 2008
"... Abstract A timedependent doublebarrier option is a derivative security that delivers the terminal value φ(ST) at expiry T if neither of the continuous timedependent barriers b ± : [0,T] → R+ have been hit during the time interval [0,T]. Using a probabilistic approach we obtain a decomposition of ..."
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Cited by 4 (1 self)
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Abstract A timedependent doublebarrier option is a derivative security that delivers the terminal value φ(ST) at expiry T if neither of the continuous timedependent barriers b ± : [0,T] → R+ have been hit during the time interval [0,T]. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions φ, barrier functions b ± and linear diffusions (St) t∈[0,T]. We show that the barrier premium can be expressed as a sum of integrals along the barriers b ± of the option’s deltas ∆ ± : [0,T] → R at the barriers and that the pair of functions (∆+,∆−) solves a system of Volterra integral equations of the first kind. We find a semianalytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the timedependent case.
Black’s Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates
 Mathematical Finance
, 2004
"... Black’s (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, al ..."
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Cited by 4 (1 self)
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Black’s (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995). When the shadow rate is modeled as a diffusion, we interpret the zerocoupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zerocoupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative.
The value of a storage facility
 Warwick Business School Working Paper, Preprint PP04142
, 2004
"... The paper derives the value of a storage facility that is too small to affect an exogenously defined price process of a storable good with seasonal and meanreverting components. It provides an elegant new continuoustime model of storage under simple assumptions, which could be applied, for example ..."
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The paper derives the value of a storage facility that is too small to affect an exogenously defined price process of a storable good with seasonal and meanreverting components. It provides an elegant new continuoustime model of storage under simple assumptions, which could be applied, for example, to natural gas. In the case without a seasonal component, closed form solutions are obtained as functions of the underlying price. A local time analysis provides an even simpler unconditional formula, which generalizes to the full model. The value of a storage facility under a model with a seasonal and a stochastic component is represented as a time integral which is easily evaluated numerically. The analysis provides a proper treatment of the true nature of the "option to store " and insights into the value of each component. An interesting feature of the model is that all transactions (whether to buy or to sell) are triggered by a single critical price. The analysis enables us to compare the profitability of storing under alternative price process assumptions. KEY WORDS real options, storage, option to store, local time. 1.