A Novel Approach to Asset Pricing with Choice of Probability Measures

Taiga Saito and Akihiko Takahashi
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Taiga Saito: Faculty of Economics, The University of Tokyo
Akihiko Takahashi: Faculty of Economics, The University of Tokyo

No CIRJE-F-1131, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper presents a foundation and concrete examples of yield curve models incorporating fundamental uncertainties, that is, uncertainties about Brownian motions representing fundamental market risks. Firstly, to model aggressive (positive)/conservative (cautious) attitudes towards such fundamental uncertainties, we consider a sup-inf/inf-sup problem on the utility of a representative agent with respect to uncertainties over Brownian motions, i.e. fundamental market risks. Secondly, we show that the problem is solved via a backward-stochastic differential equations (BSDEs) approach. Then, under a probability measure determined by solving the sup-inf/inf-sup problem, we propose interest rate models with those uncertainties and explicitly obtain their term structures of interest rates. Particularly, we present two approaches to solving the relevant coupled forward-backward stochastic differential equations (FBSDEs) to obtain expressions of the equilibrium interest rate and the term structure of interest rates. In detail, the first approach is by comparison theorems, and the second approach is to predetermine the signs of the volatilities of the BSDE in the coupled system and confirm them by explicitly solving the separated BSDE. Finally, we present concrete examples with numerical experiments.

Pages: 73 pages
Date: 2019-11
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2019cf1131

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