Control of price acceptability under the univariate Vasicek model

S. Dang-Nguyen and Y. Rakotondratsimba
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S. Dang-Nguyen: Alef-Servizi Spa, Viale Regina Margherita, 169 00199 Roma, Italy2ECE Paris Graduate School of Engineering, 37 quai de Grenelle CS71520 75 725 Paris 15, France
Y. Rakotondratsimba: Alef-Servizi Spa, Viale Regina Margherita, 169 00199 Roma, Italy2ECE Paris Graduate School of Engineering, 37 quai de Grenelle CS71520 75 725 Paris 15, France

International Journal of Financial Engineering (IJFE), 2016, vol. 03, issue 03, 1-40

Abstract: The valuation of the probability of a financial contract to be lower or higher than a given price under the univariate Vasicek model is discussed in this paper. This price restriction can be justified by consistency reasons, since some prices may not be coherent on a financial point of view, e.g. they imply negative yields, or thought as unreachable by the asset manager. At first, assuming that the pricing functions is monotone, the price constraints are formulated in terms of a threshold on the value of the spot rate process. Since this process is Gaussian, these limits are reformulated in terms of a barrier of the Gaussian increments. Next, once the thresholds are identified, the probability to satisfy the price restriction after the generation of the spot rate at one future date can be computed. Then, assuming that the bounds on the spot rate are constant during a Monte-Carlo simulation, the probability of generating a path of this process that does not satisfy the constraint is valued using some results related to the hitting times. Lastly, the proposed approach is applied to various interest rates sensitive contracts and is illustrated by some numerical examples.

Keywords: Interest rates term structure; Monte-Carlo pricing and risk management; hitting time; Vasicek model (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S2424786316500146

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