A new numerical method for tackling the three-dimensional Hestonâ??Hullâ??White partial\ndifferential equation (PDE) is proposed. This PDE has an application in pricing options when not\nonly the asset price and the volatility but also the risk-free rate of interest are coming from stochastic\nnature. To solve this time-dependent three-dimensional PDE as efficiently as possible, high order\nadaptive finite difference (FD) methods are applied for the application of method of lines. It is derived\nthat the new estimates have fourth order of convergence on non-uniform grids. In addition, it is\nproved that the overall procedure is conditionally time-stable. The results are upheld via several\nnumerical tests.
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