Results 1  10
of
15
Rational Exuberance
 Journal of Economic Literature
, 2004
"... Consider the postage stamp. As title to a future good (or, in this case, service) with monetary value, this humble object is essentially the same as a security. Its value, 37 cents, can be identiÞed with the present value of the service (delivery of a letter) to which its owner is entitled. ..."
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Cited by 28 (2 self)
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Consider the postage stamp. As title to a future good (or, in this case, service) with monetary value, this humble object is essentially the same as a security. Its value, 37 cents, can be identiÞed with the present value of the service (delivery of a letter) to which its owner is entitled.
Incomplete markets over an infinite horizon: Longlived securities and speculative bubbles
 JOURNAL OF MATHEMATICAL ECONOMICS
, 1996
"... ..."
Asset Price Bubbles in Complete Markets
"... This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no arbitrage (NFLVR) framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingale ..."
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Cited by 19 (4 self)
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This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no arbitrage (NFLVR) framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingales, and these can exist with an infinite lifetime. Type 2 bubbles are nonuniformly integrable martingales, and these can exist for a finite, but unbounded, lifetime. Last, type 3 bubbles are strict local martingales, and these can exist for a finite lifetime only. When one adds a no dominance assumption (from Merton [24]), only type 1 bubbles remain. In addition, under Merton’s no dominance hypothesis, putcall parity holds and there are no bubbles in standard call and put options. Our analysis implies that if one believes asset price bubbles exist and are an important economic phenomena, then asset markets must be incomplete.
Asset price bubbles in an incomplete market
, 2007
"... This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ..."
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Cited by 11 (2 self)
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This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ”no dominance” assumptions. We propose a new theory for bubble birth which involves a nontrivial modification of the classical framework. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices can have bubbles, but the magnitude of their bubbles must equal the magnitude of the asset’s price bubble, (iii) with no dividends, American call prices must always equal an otherwise identical European call’s price, regardless of bubbles, (iv) European putcall parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of bubbles in the underlying asset’s price. These results imply that in a market satisfying NFLVR and no dominance, in the presence of an asset price bubble, risk neutral valuation can not be used to match call option prices. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.
Strict local martingales, bubbles, and no early exercise
, 2007
"... We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula ..."
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Cited by 5 (0 self)
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We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monotonically with maturity. A complete and detailed analysis for the archetypical strict local martingale, the reciprocal of a three dimensional Bessel process, has been provided. Our main tool is based on a general htransform technique (due to Delbaen and Schachermayer) to generate positive strict local martingales. This gives the basis for a statistical test to verify a suspected bubble is indeed one (or not).
InÞnite Portfolio Strategies
, 2002
"... In inÞnitedate models the received deÞnitions of the payoffs ofÞnite portfolio strategies imply discontinuous valuation. Accordingly, in the absence of trading restrictions, arbitrage results when inÞnite trading strategies are admitted. We propose an alternative that is free of these problems. The ..."
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Cited by 1 (1 self)
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In inÞnitedate models the received deÞnitions of the payoffs ofÞnite portfolio strategies imply discontinuous valuation. Accordingly, in the absence of trading restrictions, arbitrage results when inÞnite trading strategies are admitted. We propose an alternative that is free of these problems. The alternative produces a cleaner, if more abstract, treatment of equilibrium in Þnancial models in inÞnitedate settings. We consider the bearing of the revised treatment on the theory of overlapping generations models and equivalent martingale measures. 1
Assignment Models For Constrained Marginals And Restricted Markets
 IN
, 2002
"... Duality theorems for assignment models are usually derived assuming countable additivity of the population measures. In this paper, we use finitely additive measures to model assignments of buyers and sellers. This relaxation results in more complete duality theorems and gives greater flexibilit ..."
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Cited by 1 (1 self)
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Duality theorems for assignment models are usually derived assuming countable additivity of the population measures. In this paper, we use finitely additive measures to model assignments of buyers and sellers. This relaxation results in more complete duality theorems and gives greater flexibility concerning the existence of solutions, assumptions on the spaces of agents and on profit functions. We treat two modifications of the nonatomic assignment model. In the first model, upper and lower bounds are imposed on the marginal measures representing the activities of the buyers and sellers where the lower bounds reflect a certain minimum required level of activity on the agents. In the second model, the interaction of the agents is further restricted to a certain specified subset of all matchings of buyers and sellers.
MARKET VIABILITY VIA ABSENCE OF ARBITRAGES OF THE FIRST
, 904
"... Abstract. The absence of arbitrages of the first kind, a weakening of the “No Free Lunch with Vanishing Risk ” condition of [2], is analyzed in a general semimartingale financial market model. In the spirit of the Fundamental Theorem of Asset Pricing, it is shown that there is equivalence between th ..."
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Abstract. The absence of arbitrages of the first kind, a weakening of the “No Free Lunch with Vanishing Risk ” condition of [2], is analyzed in a general semimartingale financial market model. In the spirit of the Fundamental Theorem of Asset Pricing, it is shown that there is equivalence between the absence of arbitrages of the first kind and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes. One of the cornerstones of Mathematical Finance theory is the celebrated Fundamental Theorem of Asset Pricing (FTAP) that connects the economically sound notion of absence of opportunities for riskless profit with the mathematical condition of the existence of a probability measure, equivalent to the realworld one, that makes the discounted asset prices have some kind of martingale property.
Investor Irrationality and the Nasdaq Bubble ∗
"... We exploit the information in the options market to study the risk and risk premium variations around the Nasdaq bubble period. In particular, we investigate whether the dramatic rise and fall of the Nasdaq can be justified by changes in return risk, or there were corresponding unusual shifts in how ..."
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We exploit the information in the options market to study the risk and risk premium variations around the Nasdaq bubble period. In particular, we investigate whether the dramatic rise and fall of the Nasdaq can be justified by changes in return risk, or there were corresponding unusual shifts in how investors price risks. We specify a model that accommodates fluctuations in both risk levels and market prices of different sources of risks, and we estimate the model using timeseries returns and option prices on the Nasdaq 100 index. Our analysis reveals three key pieces of evidence that foretell the arrival and burst of a bubble. First, during the Nasdaq bubble period, return volatility increased together with the rising index level, even though the two tend to move in opposite directions in general. Second, while the market price of volatility risk is strongly negative historically as investors dislike high volatility levels and volatility risk, the market price of volatility risk declined in absolute magnitude and approached zero at the end of 1999. In contrast to the average risk premium at normal market conditions, aversion to volatility risk completely disappeared during the height of the bubble period. Third, the options market showed an increasing market price of downside jump risk that peaked three month prior to the bursting of the bubble, highlighting the increasing demand for hedging against the potential crash of the Nasdaq market valuation. On the other hand, the market price of the downside jump