Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/253513 
Year of Publication: 
2021
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 16 [Issue:] 1 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2021 [Pages:] 25-47
Publisher: 
The Econometric Society, New Haven, CT
Abstract: 
We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ''markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and (b) the largest possible one-period step in the discrete-time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected-utility-maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete-time economies as she can at the continuous-time limit. Hence, in economically significant ways, many discrete-time models with frequent trading resemble the complete-markets model of BSM.
Subjects: 
Market completeness
Black-Scholes-Merton model
synthesis of contingent claims
JEL: 
D0
G0
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article

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