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Expansion method to value forex options based on stochastic volatility and interest rates

By on July 20, 2021 0
















































Expansion method for valuing forex options under stochastic volatility and interest rates – Journal of Computational Finance





  • Approximation formula for pricing options in the Heston-Hull-White model
  • Asymptotic development up to the second order based on the Malliavin calculus
  • Control variant improving accuracy for high volatility volatility
  • Precision numerically comparable with another method using the characteristic function approximation

Some expansion methods have been proposed for pricing options in roughly analytical form. One of them is the smart expansion method based on Malliavin’s calculus, which is used to price options in the Heston stochastic volatility model with deterministic interest rates. In this paper, we apply the method to the Heston-Hull-White model, which admits stochastic interest rates to improve the model, and we obtain the expansion formula for pricing options in the model up to the second order. . Then, numerical studies are performed to compare our approximation formula with the Monte Carlo simulation. Our formula shows numerically comparable results with another method using the characteristic function approximation, and can also be applied for parameter configurations where the latter method is not useful. The control variable is also used to improve the accuracy of high volatility volatility cases.