خلاصة:
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.
ملخص الجهاز:
This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk minimizing portfo- lio.
The hedging problem in such environment is a very challenging issue in financial mathematics, be- cause the market driven by these processes is incomplete; this means that associated with any hedging portfolio there is an unchangeable (residual) risk.
The local risk minimization (LRM) and the mean-variance (MV) are two major quadratic methods for hedging, which the former one focuses on the admissibility and the later one emphasizes on the self-financing property, respectively, for more approaches refer to chapter 10 of [1].
We conclude that in a continuous word when the jumps are limited to 0 , both assumptions of independence and correlation of assets lead to a same hedging portfolio.
It shows that in a continuous market, the hedging portfolio is independent of correlation parameters and is equal to )VIew the image of this page) (i 1,, m) , whether the assets are independent or correlated.