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Speculation and bubbles: The case of finitely lived assets| old_uid | 13671 |
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| title | Speculation and bubbles: The case of finitely lived assets |
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| start_date | 2014/03/25 |
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| schedule | 15h |
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| online | no |
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| location_info | salle 11 |
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| summary | The history of financial markets is strewn with periods in which asset prices seem to vastly exceed fundamentals—events commonly called bubbles. Nonetheless, there is very little agreement among economists on the economic forces that generate such occurrences. Part of the difficulty stems from the fact that economists’ discussions of bubbles often concentrate solely on the behavior of asset prices. The most common definition of a bubble is “a period in which prices exceed fundamental valuation.” Valuation, however, depends on a view of fundamentals, and efficient-market advocates correctly point out that valuations are almost always, ex post, wrong.
In this lecture I will discuss some other stylized facts that are associated with bubble episodes, in particular the increase in trading volume that often accompany bubbles. I will argue that a model that combines differences in beliefs with asymmetries between the cost of acquiring an asset and the cost of shorting that same asset can explain the correlation between bubbles and trading.
I will present a mathematical model developed with H. Berestycki and R. Monneau that allows for assets with a finite life, such as many credit instruments. In the model, the buyer of the asset today acquires also an option to resell that asset to other more optimistic traders in the future. In equilibrium, buyers would be part of the most optimistic group but would be willing to pay in excess of their optimistic views, because they value the option to resell. The value of this option can be legitimately called a bubble. The resale option is American - that is it can be exercised at any time before the expiration of the asset. Thus the value of the resale option is given by an associated optimal stopping time but the value of stopping in turn is given by a stopping time problem faced by the new buyer. Because of this recursive aspect in the option valuation, the value of the option is characterized by a nonlocal obstacle problem. The equilibrium value of the option to resell corresponds to the viscosity solution of the obstacle problem and we establish several properties of this solution in the paper.
I will discuss the effects of parameters such as interest rates or transaction costs on the magnitude of the bubble and trading volume. In particular, I will argue that a small Tobin tax while effective in lowering trading volume is unlikely to have much of an effect on the size of the bubble. |
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| responsibles | Berestycki, Nadal, Rosenstiehl |
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