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14
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 136 (11 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 46 (1 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 12 (2 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
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.
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.
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 3 (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
Valuing European options when the terminal value of the underlying asset is unobservable
, 1991
"... This paper has benefitted greatly from my discussions with Jennie France. Also, ..."
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Cited by 2 (0 self)
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This paper has benefitted greatly from my discussions with Jennie France. Also,
On the Nature of Options
, 2000
"... We consider the role of options when markets in its underlying asset are frictionless and when this underlying has a volatility process and jump arrival rates which are arbitrarily stochastic. By combining a static option position with a particular dynamic hedging strategy, we characterize the optio ..."
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Cited by 1 (0 self)
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We consider the role of options when markets in its underlying asset are frictionless and when this underlying has a volatility process and jump arrival rates which are arbitrarily stochastic. By combining a static option position with a particular dynamic hedging strategy, we characterize the option's time value as the (riskneutral) expected benefit from being able to buy or sell one share of the underlying at the option's strike whenever the strike price is crossed. The buy/sell decision can be based on the post jump price, so that a rational investor buys on rises and sells on drops. Thus, an option provides liquidity at its strike even when the market doesn't. We next present two methods for extending this local liquidity to every price between the pre and post jump level. The first method involves holding a continuum of options of all strikes. The second method holds one option, but adjusts the dynamic hedging strategy. We discuss the advantages and disadvantages of each approach...
On the Nature of Options
, 2000
"... We consider the role of options when markets in its underlying asset are frictionless and when this underlying has a volatility process and jump arrival rates which are arbitrarily stochastic. By combining a static option position with a particular dynamic hedging strategy, we characterize the optio ..."
Abstract
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We consider the role of options when markets in its underlying asset are frictionless and when this underlying has a volatility process and jump arrival rates which are arbitrarily stochastic. By combining a static option position with a particular dynamic hedging strategy, we characterize the option's time value as the (riskneutral) expected benefit from being able to buy or sell one share of the underlying at the option's strike whenever the strike price is crossed. The buy/sell decision can be based on the post jump price, so that a rational investor buys on rises and sells on drops. Thus, an option provides liquidity at its strike even when the market doesn't. We next present two methods for extending this local liquidity to every price between the pre and post jump level. The first method involves holding a continuum of options of all strikes. The second method holds one option, but adjusts the dynamic hedging strategy. We discuss the advantages and disadvantages of each approach...
Jesper Andreasen Peter Carr
"... this paper adds one more. We derive a new result termed Put Call Reversal (PCR) which relates the value of a European call to the value of a European put written on a price process which runs backward in time. The result is modeldependent and assumes that the usual forwardrunning stock price pr ..."
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this paper adds one more. We derive a new result termed Put Call Reversal (PCR) which relates the value of a European call to the value of a European put written on a price process which runs backward in time. The result is modeldependent and assumes that the usual forwardrunning stock price process S is a jump di#usion, where lognormal volatility is bounded and where the jump part of the returns process has independent increments. We also assume that the riskfree rate and dividend yield are deterministic. Let C(t 0 , S 0 ; T, K) be the value at time t 0 given that S t 0 = S 0 0 of a European call written on process S with maturity T t 0 and strike K 0. Consider some economy in which time runs backwards. Since the forward running process S is Markov in itself, the backward running process S is Markov in itself. In the backward economy, let t 0 , S 0 ; be the value at the reverse time t 0 given S t 0 = S 0 0 of a European put written on the process S with maturity t and strike 0. Then PCR is: C(t 0 , S 0 ; T, K) = P (T, K; t 0 , S 0 ), S 0 , K t 0 . (1) In words, at t = t 0 , a call on the forward running process S started at S t 0 = S 0 with maturity T and strike K has the same value at the reverse time t = T as a put on a backward running process S started at S t 0 = K, where the put matures at t = t 0 and has strike K = S 0 . The valuation date for the put is the maturity date of the call and vice versa. Hence, the two options have the same time to maturity on their respective valuation dates. Note that the call's strike price is the price for the put's underlying on the put's valuation date. Analogously, the price of the call's underlying on the call's valuation date is the put's strike price. Ther...