The Pricing of Equity-Linked Contingent Claims Under a Lognormal Short Rate Dynamics

Posted: 14 Apr 2011

See all articles by Rosa Cocozza

Rosa Cocozza

University of Naples Federico II - Faculty of Economics

Antonio De Simone

University of Naples Federico II - Faculty of Economics

Date Written: April 12, 2011

Abstract

We propose a numerical procedure for the pricing of financial contracts whose contingent claims are exposed to two sources of risk: the stock price and the short interest rate. More precisely, in our pricing framework we assume that the stock price dynamics is described by the Cox, Ross Rubinstein (CRR, 1979) binomial model under a stochastic risk free rate, whose dynamics evolves over time accordingly to the Black, Derman and Toy (BDT, 1990) one-factor model. To this aim, we set the hypothesis that the instantaneous correlation between the trajectories of the future stock price (conditional on the current value of the short rate) and of the future short rate is zero and we therefore show that the hypothesis of absence of instantaneous correlation between the two mentioned risk factors does not necessarily imply that also their terminal correlation is zero. We then apply the resulting stock price dynamics to evaluate the price of a simple contract, i.e. of a stock option. Finally, we compare the derived price to the price of the same option under different pricing models, as the traditional Black and Scholes (1973) model. We expect that, the difference in the two prices is not sensibly large. We conclude showing in which cases it should be helpful to adopt the described model for pricing purposes.

Keywords: option pricing, stochastic short rate model, binomial tree

JEL Classification: C63, C65, G13

Suggested Citation

Cocozza, Rosa and De Simone, Antonio, The Pricing of Equity-Linked Contingent Claims Under a Lognormal Short Rate Dynamics (April 12, 2011). Available at SSRN: https://ssrn.com/abstract=1807986

Rosa Cocozza (Contact Author)

University of Naples Federico II - Faculty of Economics ( email )

Via Cintia Monte S. Angelo
Napoli, 80126
Italy
+39/81675083 (Phone)

HOME PAGE: http://www.docenti.unina.it/rosa.cocozza

Antonio De Simone

University of Naples Federico II - Faculty of Economics ( email )

Via Cintia, Monte S. Angelo
Napoli, 80126
Italy

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