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

PDF
MPRA_paper_30859.pdf Download (294kB)  Preview 
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:  24. Feb 2015 09:14 
References:  Amin, K. I., Jarrow, R. A. (1992). Pricing options on risky assets in a stochastic interest rate economy. Mathematical Finance, 2(4), 217237. Bacinello, A. R., Ortu, F. (1996). Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results. European Journal of Operational Research, 91(2), 235249. Black, F. (1976). The pricing of commodity contracts. The Journal of Political Economy, 3(12), 167179. Black, F., Derman, E., Toy, W. (1990).A onefactor model of interest rates and its application to treasury bond options. Financial Analysts Journal, 46(1), 3339. Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637654. Brace, A., Gątarek, D., Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127155. Brennan, M. J., Schwartz, E. S. (1976). The pricing of equitylinked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3(3), 159213. Brennan, M. J., Schwartz, E. S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15(4), 907929. Cox, J. C., Ross, S. A., Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229263. Cox, J. C., Ingersoll, J. E., Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385407. Cocozza, R., Orlando, A. (2009). Managing structured bonds: An analysis using RAROC and EVA. Journal of Risk Management in Financial Institutions, 2(4), 409426. Cocozza, R., De Simone, A., Di Lorenzo, E., Sibillo, M. (2011). Participating policies: Risk and value drivers in a financial management perspectives. Forthcoming in the 14th Conference of the ASMDA International Society, 710 June 2011. De Simone, A. (2010). Pricing interest rate derivatives under different interest rate modeling: A critical and empirical analysis. Investment Management and Financial Innovations, 7(2), 4049. Feller, W. (1951). Two singular diffusion problems. Annals of Mathematics, 54(1), 173182. Ho, T. S. Y., Lee, S.B. (1986). Term structure movements and pricing interest rate contingent claims. The Journal of Finance, XLI(5), 10111029. Hull, J. C. (2009). Options, futures and other derivatives. Prentice Hall. Kim, Y.J., Kunitomo, N. (1999). Pricing options under stochastic interest rates: A new approach. AsiaPacific Financial Markets, 6(1), 4970. Kunitomo, N., Kim, Y.J. (2001). Effects of stochastic interest rates and volatility on contingent claims. CIRJEF 129 (Extended Version of CIRJEF67, 2000), University of Tokyo. Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141183. Neftci, S. (2008). Principles of financial engineering. Academic Press, Advanced Finance Series. Rabinovitch, R. (1989). Pricing stock and bond options when the defaultfree rate is stochastic. Journal of Financial and Quantitative Analysis, 24(4), 447457. Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177188. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/30859 