2 research outputs found
Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method
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 It\^{o}'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 terms, which makes its
difficult to solve it analytically. Also, a standard approach of solving it
numerically by using traditional finite--difference (FD) or finite elements
(FE) methods suffers from the high computational burden. Therefore, in this
paper a flavor of a localized radial basis functions (RBFs) method, RBF--FD, is
developed which allows for a good accuracy at a relatively low computational
cost. Results of numerical simulations are presented which demonstrate
efficiency of such an approach in terms of both performance and accuracy for
pricing FX options and computation of the associated Greeks.Comment: 24 pages, 7 tables, 4 figure
Four-factor model of Quanto CDS with jumps-at-default and stochastic recovery
In this paper we modify the model of Itkin, Shcherbakov and Veygman, (2019)
(ISV2019), proposed for pricing Quanto Credit Default Swaps (CDS) and risky
bonds, in several ways. First, it is known since the Lehman Brothers bankruptcy
that the recovery rate could significantly vary right before or at default,
therefore, in this paper we consider it to be stochastic. Second, to reduce
complexity of the model, we treat the domestic interest rate as deterministic,
because, as shown in ISV2019, volatility of the domestic interest rate does not
contribute much to the value of the Quanto CDS spread. Finally, to solve the
corresponding systems of 4D partial differential equations we use a different
flavor of the Radial Basis Function (RBF) method which is a combination of
localized RBF and finite-difference methods, and is known in the literature as
RBF-FD. Results of our numerical experiments presented in the paper demonstrate
that the influence of volatility of the recovery rate is significant if the
correlation between the recovery rate and the log-intensity of the default is
non-zero. Also, the impact of the recovery mean-reversion rate on the Quanto
CDS spread could be comparable with the impact due to jump-at-default in the FX
rate.Comment: 30 pages, 7 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1711.0713