A highly efficient pricing method for European-style options based on Shannon wavelets

In the search for robust, accurate and highly efficient financial option valuation techniques, we present here the SWIFT method (Shannon Wavelets Inverse Fourier Technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. The nature of the local Shannon wavelets basis enables us to adaptively determine the proper size of the computational interval. Numerical experiments on European-style options confirm the bounds, robustness and efficiency

Pricing early-exercise and discrete barrier options by Shannon wavelet expansions

We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods

Quantifying credit portfolio losses under multi-factor models

In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords

On the data-driven COS method

In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based finan- cial option valuation method which assumes the availability of asset data samples: a char- acteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O(1 / √ n ) , in line with Monte Carlo meth- ods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option’s sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods

Efficient Wrong-Way Risk Modelling for Funding Valuation Adjustments

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, it can be challenging to compute WWR efficiently. We propose to split the relevant exposure profile into two parts: an independent part and a WWR-driven part. For the first part, already available exposures can be used where correlations between the funding spread and market risks are ignored. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. The proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modelling. Furthermore, the approximation provides some intuition on WWR. Case studies are presented for an interest rate swap and a representative multi-currency portfolio of swaps. They illustrate that the approximation method is applicable in a practical setting due to its generic nature. We analyze the approximation error and illustrate how the approximation can be used to compute WWR sensitivities, which are needed for risk management