ADI Finite Difference Methods for Heston–Hull–White Option Pricing

Summary

The paper studies alternating direction implicit time-stepping methods for numerically solving the three-dimensional Heston–Hull–White partial differential equation. It first discretizes space with finite differences on nonuniform grids, then assesses ADI schemes for the time dimension. The model includes stochastic volatility and interest rates, and the analysis permits arbitrary correlations and time-varying mean-reversion levels.

The tests cover European calls and up-and-out calls, short and long maturities, and parameter settings both inside and outside the Feller condition. The reported experiments indicate that ADI methods can be stable, accurate, and efficient when their parameters are chosen appropriately across these cases. This is numerical evidence about solving the pricing equation, rather than a claim about trading performance. The document does not provide specific parameter recommendations or quantified error and runtime results, so implementation choices still require problem-specific validation.

Key ideas

• The study applies ADI time discretization to a three-dimensional Heston–Hull–White pricing equation.
• Finite differences on nonuniform spatial grids provide the spatial discretization.
• The tests include arbitrary correlations and time-varying mean-reversion levels.
• European calls and up-and-out calls are evaluated across varied maturities and Feller-condition cases.
• The reported performance depends on choosing suitable ADI parameters.

Tags

# ADI finite difference schemes for the Heston-Hull-White PDE


# ADI finite difference schemes for the Heston-Hull-White PDE









In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.