We assume that the jump arrival intensity falls in the interval of [10, 50], the jump volatility in the interval of [0.0537, 0.1537], and the correlation parameters measuring the basis risks, [[rho].sub.sf] and [[rho].sub.XA], are within simulated values between 0 and 1 with the condition that [[rho].sub.XA] > [[rho].sub.sf], ceteris paribus.
Sensitivity analysis concludes the research by exploring the impact of basis risk, variable hedging cost, jump volatility, and jump intensity on hedging effectiveness.
Now assuming there is no basis risk between the change in the cash and the futures prices to circumvent the issue of stochastic interest rates and that the futures price function is twice continuously differentiable in the underlying factor values, c and j, we next derive the futures price process below by applying the generalized Ito's lemma to the function with respect to Equations (1) and (3),
These two coefficients measure the basis risk in our cross-hedging effectiveness evaluation as the changes of the firm's total loss and the CHI value would not be perfectly correlated when a catastrophic event occurs--the former depends on both physical and nonphysical factors whereas the latter depends on physical factors of the hurricane only.
Let [C.sub.i,t] represent the aggregate loss for issuing firm i and, to estimate the impact of basis risks on the CAT bond price, [C.sub.index,t] represents that for a composite index of losses (e.g., a PCS index).
Having different values for the index and individual insurers can be done without further difficulties, but it increases the dimension of calculation and does not provide more insights to this analysis of basis risks. The analysis will focus on the coefficient of correlation between the individual loss and the loss index, [[rho].sub.x], rather than on their means and standard deviations.
Table 4 examines the impact of basis risks on CAT bond prices.
(8.) Because the difference caused by the interest rate elasticity is small, the authors report only the case of [phi] = -3 and focus the discussion on basis risks.