Related papers: Chebyshev Methods for Ultra-efficient Risk Calcula…
Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives are priced via Monte Carlo simulation: in…
Exposure simulations are fundamental to many xVA calculations and are a nested expectation problem where repeated portfolio valuations create a significant computational expense. Sensitivity calculations which require shocked and unshocked…
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for…
We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev…
In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\lambda$). We propose an efficient way to interpolate the…
Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently,…
When the Orthogonal Chebyshev Sliding Technique was introduced it was applied to a portfolio of swaps and swaptions within the context of the FRTB-IMA capital calculation. The computational cost associated to the computation of the ES…
This paper concerns the design of a multidimensional Chebyshev interpolation based method for a differential game theory problem. In continuous game theory problems, it might be difficult to find analytical solutions, so numerical methods…
Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation…
Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the butterfly algorithm considered here realizes the transfer…
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the…
A fast multipole method (FMM) for asymptotically smooth kernel functions (1/r, 1/r^4, Gauss and Stokes kernels, radial basis functions, etc.) based on a Chebyshev interpolation scheme has been introduced in [Fong et al., 2009]. The method…