Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models |
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| Institution: | 1. London Business School, Institute of Finance, Sussex Place, Regents Park, London NWI 4SA, UK;2. Columbia University, New York, United States;3. CEPR, London, UK;4. Universita’ Bocconi, Istituto di Metodi Quantitativi, Viale Isonzo 25, 20100 Milan, Italy;1. University of St.Gallen, Swiss Institute of Banking and Finance (s/bf), Rosenbergstrasse 52, 9000 St. Gallen, Switzerland;2. EBS Business School, Department of Finance, Accounting and Real Estate, Gustav-Stresemann-Ring 3, 65189 Wiesbaden, Germany;3. Macquarie Capital (Europe) Limited, OpernTurm, Bockenheimer Landstrasse 2-4, 60306 Frankfurt, Germany;1. School of Economics and Management, University of Firenze, Italy;2. Department of Mathematical Stochastics, University of Freiburg, Freiburg, Germany;1. Goodman School of Business, Brock University, Canada;2. Department of Economics, Vassar College, USA;3. Schulich School of Business, York University, Canada;1. Department of Accountancy and Finance, School of Business, University of Otago, PO Box 56, Dunedin 9054, New Zealand;2. Miyazaki International College, 1405 Kano, Kiyotake, Miyazaki 889-1605, Japan |
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| Abstract: | A widespread approach in the implementation of asset pricing models is based on the periodic recalibration of its parameters and initial conditions to eliminate any conflict between model-implied and market prices. Modern no-arbitrage market models facilitate this procedure since their solution can usually be written in terms of the entire initial yield curve. As a result, the model fits (by construction) the interest rate term structure. This procedure is, however, generally time inconsistent since the model at time t = 0 completely specifies the set of possible term structures for any t > 0. In this paper, we analyze the pros and cons of this widespread approach in pricing and hedging, both theoretically and empirically. The theoretical section of the paper shows (a) under which conditions recalibration improves the hedging errors by limiting the propagation of an initial error, (b) that recalibration introduces time-inconsistent errors that violate the self-financing argument of the standard replication strategy. The empirical section of the paper quantifies the trade-off between (a) and (b) under several scenarios. First, we compare this trade-off for two economies with and without model specification error. Then, we discuss the trade-off when the underlying economy is not Markovian. |
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