Pricing Interest Rate Contingent Claims in Markets with Uncertain Volatility

Posted: 3 Nov 1998

See all articles by Pawel Lewicki

Pawel Lewicki

J.P. Morgan Chase Securities Inc.

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Abstract

We consider a financial market where the volatility of the interest rate is not known exactly, but rather it is assumed to lie within two a-priori known bounds. These bounds represent the extreme values of the volatility implied by traded options. In this market, the interest rate process which allows no arbitrage and fits exactly the initial term structure of the forward interest rates, is not determined uniquely: for each volatility path in a band between the minimal and maximal volatility, there exists a different interest rate process. The asking and the bidding prices in our model are functions of the time, the interest rate, and the accumulated volatility, and they satisfy a new non-linear partial differential pricing equation. In this equation, the volatility used for pricing a claim is chosen dynamically: it is either the minimal or the maximal volatility depending on the claim's curvature with respect to both the interest rate and the accumulated volatility. We compare our model to the standard Ho-Lee model. We illustrate the effectiveness of our pricing scheme with numerical calculations for a calendar spread.

JEL Classification: E43

Suggested Citation

Lewicki, Pawel and Avellaneda, Marco, Pricing Interest Rate Contingent Claims in Markets with Uncertain Volatility. Available at SSRN: https://ssrn.com/abstract=5940

Pawel Lewicki (Contact Author)

J.P. Morgan Chase Securities Inc.

270 Park Avenue
New York, NY 10027
United States

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

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United States
212-998-3129 (Phone)
212-995-4121 (Fax)

Finance Concepts LLC ( email )

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