Cocozza, Rosa and De Simone, Antonio (2011): One numerical procedure for two risk factors modeling.

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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) onefactor 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. 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.
Item Type:  MPRA Paper 

Original Title:  One numerical procedure for two risk factors modeling 
Language:  English 
Keywords:  option pricing; stochastic short rate model; binomial tree 
Subjects:  G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing; Trading volume; Bond Interest Rates C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing; Futures Pricing 
Item ID:  30859 
Depositing User:  Rosa Cocozza 
Date Deposited:  13. May 2011 11:32 
Last Modified:  13. Feb 2013 09:57 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/30859 