Pricing derivatives with barriers in a stochastic interest rate environment

This paper develops a general valuation approach to price barrier options when the term structure of interest rates is stochastic. These products’ barriers may be constant or stochastic, in particular we examine the case of discounted barriers (at the instantaneous interest rate). So, in practice, w...

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Bibliographic Details
Published in:Journal of economic dynamics & control 2008-09, Vol.32 (9), p.2903-2938
Main Authors: Bernard, Carole, Le Courtois, Olivier, Quittard-Pinon, François
Format: Article
Language:English
Subjects:
Approximation
Barrier option
Change of Numéraire
Derivatives
Interest rates
Markovian approximation
Markovian processes
Pricing
Securities prices
Stochastic models
Stochastic processes
Studies
Term structure
Valuation
Vasicek model
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Summary:This paper develops a general valuation approach to price barrier options when the term structure of interest rates is stochastic. These products’ barriers may be constant or stochastic, in particular we examine the case of discounted barriers (at the instantaneous interest rate). So, in practice, we extend Rubinstein and Reiner [1991. Breaking down the barriers. Risk 4(8), 28–35], who give closed-form formulas for pricing barrier options in a Black and Scholes context, to the case of a Vasicek modeling of interest rates. We are therefore in the situation of pricing barrier options semi-explicitly or explicitly (depending on the shape of the barrier) with stochastic Vasicek interest rates. The model is illustrated with a specific contract, an up and out call with rebate, hence a typical barrier option. This example is merely here to show how any standard barrier option can be priced and its Greeks be obtained in such a context. The validity of the approximation is analyzed and the sensitivity to the barrier level and to discretization schemes are also derived.
ISSN:0165-1889
1879-1743
DOI:10.1016/j.jedc.2007.11.004