Pricing foreign exchange options under stochastic volatility and interest rates using an RBF-FD method

@article{Soleymani2019PricingFE,
  title={Pricing foreign exchange options under stochastic volatility and interest rates using an RBF-FD method},
  author={Fazlollah Soleymani and Andrey Itkin},
  journal={J. Comput. Sci.},
  year={2019},
  volume={37}
}
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an Ito's diffusion with time--dependent drift, and with a full matrix of correlations. It is known that prices of FX options in this model can be found by solving an associated backward partial differential equation (PDE). However, it contains non--affine… Expand
Four-factor model of Quanto CDS with jumps-at-default and stochastic recovery
TLDR
The model of Itkin, Shcherbakov and Veygman, (2019) (ISV2019), proposed for pricing Quanto Credit Default Swaps and risky bonds, is modified in several ways to reduce complexity and to solve the corresponding systems of 4D partial differential equations using a different flavor of the Radial Basis Function (RBF) method. Expand
On the Statistical GARCH Model for Managing the Risk by Employing a Fat-Tailed Distribution in Finance
TLDR
The extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, and this distribution is employed in investigating explicit formulas for the two common risk measures, i.e., VaR and CVaR to have better tools in risk management. Expand
Numerical study of the nonlinear anomalous reaction-subdiffusion process arising in the electroanalytical chemistry
TLDR
A meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD) that provides accurate solutions on complex domains with any distribution node type. Expand
Constructing the weighting coefficients for the RBF-Hermite FD scheme under the multiquadric function on irregular meshes
It is well known that the order of finite difference estimates on nonuniform grids reduce dramatically, particularly when higher order derivatives are required. This paper contributes how anExpand

References

SHOWING 1-10 OF 80 REFERENCES
The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach
TLDR
Numerical experiments are presented showing that the option pricing algorithm developed in this paper is extremely accurate and fast and significantly more efficient than other numerical methods that have recently been proposed for pricing American options under the Bates model. Expand
Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates
Abstract Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate combined with the Cox et al. dynamics for the domestic and foreign stochastic interestExpand
On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates
Abstract We construct multi-currency models with stochastic volatility (SV) and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX)Expand
Radial Basis Function generated Finite Differences for option pricing problems
TLDR
A numerical method to price options based on Radial Basis Function generated Finite Differences (RBF-FD) in space and the Backward Differentiation Formula of order 2 (BDF-2) in time, which provides high computational efficiency and accuracy. Expand
Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methods
TLDR
The useful features of the proposed Radial Basis Function methods, such as high accuracy, sparsity of the differentiation matrices, mesh-free nature and multi-dimensional extendability, are demonstrated, and how to apply them for solving time-dependent higher-dimensional PDEs in finance are demonstrated. Expand
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility andExpand
Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility
We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-termExpand
Pricing currency options in the Heston/CIR double exponential jump-diffusion model
We examine currency options in the double exponential jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreignExpand
Improved radial basis function methods for multi-dimensional option pricing
In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black-Scholes partial differential equation. As an example of aExpand
Pricing FX Options in the Heston/CIR Jump-Diffusion Model with Log-Normal and Log-Uniform Jump Amplitudes
We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump amplitudes and the volatility model withExpand
...
1
2
3
4
5
...