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21
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 39 (6 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 33 (4 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.
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 31 (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
"... ..."
Finitely Additive Probabilities and the Fundamental Theorem of Asset
 Pricing, in Contemporary Quantitative Finance
, 2010
"... Abstract This work aims at a deeper understanding of the mathematical implications of the economicallysound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that the absence of arbitrages ..."
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Cited by 26 (7 self)
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Abstract This work aims at a deeper understanding of the mathematical implications of the economicallysound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that the absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become “local martingales”. The aforementioned result is then used to obtain an independent proof of the classical FTAP, as it appears in Delbaen and Schachermayer (Math. Ann. 300:463–520, 1994). Finally, an elementary and short treatment of the previous discussion is presented for the case of continuouspath semimartingale assetprice processes. 1
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 7 (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).
An analysis of the doubling strategy: The countable case. reproduced, Federal Reserve Bank of Atlanta
, 2002
"... Abstract. We analyze the doubling strategy in static and dynamic settings with a countable state space. We apply the noarbitrage and nofreelunch definitions of Kreps (1981), which (in the dynamic setting) put the focus on the gain produced by a selffinancing trading strategy, rather than on the ..."
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Cited by 1 (0 self)
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Abstract. We analyze the doubling strategy in static and dynamic settings with a countable state space. We apply the noarbitrage and nofreelunch definitions of Kreps (1981), which (in the dynamic setting) put the focus on the gain produced by a selffinancing trading strategy, rather than on the strategy itself. By applying the Krepsian notions of no arbitrage and no free lunches to dynamic models, instead of the notions common in standard practice, we avoid the situation where there are no free lunches at the same time there are arbitrage opportunities. Depending on the topological space one adopts, the doubling strategy is either (i) not in the space of payouts (and hence not a free lunch), (ii) in the space and a free lunch, or (iii) in the space but not a free lunch. In the latter case, which requires ‘near riskneutrality’, the doubling strategy has a bubble component in the sense of Gilles and LeRoy (1997).
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.
unknown title
, 2008
"... Analysis of continuous strict local martingales via htransforms ..."
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