Technical paper/Finite difference methods
An artificial neural network representation of the SABR stochastic volatility model
In this paper the universal approximation theorem of artificial neural networks (ANNs) is applied to the stochastic alpha beta rho (SABR) stochastic volatility model in order to construct highly efficient representations.
Pricing American call options using the Black–Scholes equation with a nonlinear volatility function
In this paper, the authors investigate a nonlinear generalization of the Black–Scholes equation for pricing American-style call options, where the volatility term may depend on both the underlying asset price and the Gamma of the option.
Hybrid finite-difference/pseudospectral methods for the Heston and Heston–Hull–White partial differential equations
In this paper, the authors propose a hybrid spatial finite-difference/pseudospectral discretization for European option-pricing problems under the Heston and Heston–Hull–White models.
Adjoint algorithmic differentiation tool support for typical numerical patterns in computational finance
This paper demonstrates the flexibility and ease in using C++ algorithmic differentiation (AD) tools based on overloading to numerical patterns (kernels) arising in computational finance.
Monte Carlo payoff smoothing for pricing autocallable instruments
This paper develops a Monte Carlo method to price instruments with discontinuous payoffs and non-smooth trigger functions, which allows a stable computation of Greeks via finite differences.
A hybrid tree/finite-difference approach for Heston–Hull–White-type models
In this paper, the authors study a hybrid tree/finite-difference method, which allows us to obtain efficient and accurate European and American option prices in the Heston–Hull– White and Heston–Hull–White2d models.
Finite difference techniques for arbitrage-free SABR
This paper applies a variety of second-order finite difference schemes to the SABR arbitrage-free density problem and explores alternative formulations.
Finite difference methods for estimating marginal risk contributions in asset management
This paper studies the use of finite difference methods for estimating risk contributions.
A novel partial integrodifferential equation-based framework for pricing interest rate derivatives under jump-extended short-rate models
Interest rate derivatives under jump-extended short-rate models have commonly been valued using lattice methods. This paper proposes a much faster and more accurate valuation method based on partial integrodifferential equations.
Numerical algorithms for research and development stochastic control models
The authors consider the optimal strategy of research and development (R&D) expenditure adopted by a firm that engages in R&D to develop an innovative product to be launched in the market.
Options for collateral options
Options for collateral options