Hedging of Options in Jump-Diffusion Markets with Correlated Assets
محورهای موضوعی : Financial Mathematics
1 - Iran University of Science and Technology
کلید واژه: Hedging option, Locally Risk Minimizing approach, Correlated assets, Residual risk,
چکیده مقاله :
We consider the hedging problem in a jump-diffusion market with correlated assets. For this purpose, we employ the locally risk-minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk-minimizing portfolio. In addition, we investigate the sensitivity of the risk with respect to the variation of correlation parameters, this enables us to select the more profitable portfolio. The results show that the risk increases, with increasing the correlation parameters. This means that to reduce risk it is necessary to invest in low correlated assets.
[1] Cont, R., Tankov, P., Financial modelling with jump processes, Financial Mathematics Series, Chapman and Hall/CRC, 2004.
[2] Markowitz, H., Portfolio Selection: Efficient diversification of investments, Yale University Press, 16, 1959.
[3] Bauerle, N., Risk management in credit risk portfolios with correlated assets, Insurance Mathematical Economic, 2002, 30, P.187-198.
[4] Christodoulakis, G.A., Satchell, S.E., Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns, European Journal of Operational Research, 2002, 139, P. 351-370.
[5] Windcliff, H., Wang, J., Forsythb, P.A., Vetzal, K.R., Hedging with a correlated asset: Solution of a nonlinear pricing PDE, Journal of Computational and Applied Mathematics 200, 2007, P. 86-115.
[6] Raffaelli, G., Marsili, M., Dynamic instability in a phenomenological model of correlated assets, Journal of Statistical Mechanics: Theory and Experiment, 2006, P.1-9, Online at stacks.iop.org/JSTAT/2006/L08001.
[7] Coaker, W. J., Emphasizing Low-Correlated Assets: The Volatility of Correlation, Journal of Financial Planning, 2007, P. 52-70.
[8] Izadikhah, M., Improving the Banks Shareholder Long Term Values by Using Data Envelopment Analysis Model, Advances in Mathematical Finance and Applications, 2018, 3(2), P. 27-41.Doi: 10.22034/amfa.2018.540829
[9] Schweizer, M., Option hedging for semimartingales, Stochastic Process with Application, 1991, 37, P. 339-363.
[10] Follmer, H., Schweizer, M., Hedging of contingent claims under incomplete information, Applied Stochastic Analysis, Stochastic Monographs, 5, Goldon and Breach, 1991, P. 389- 414.
