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The Alternating Direction Explicit (ADE) Method for One-Factor Problems: Wilmott Magazine Article
Guillaume Pealat and Daniel J. Duffy 718 Views

In this article we apply the ADE method to a number of partial differential equations in option pricing using one-factor models (Black-Scholes, local volatility, uncertain volatility).
xVA - Coping with the Tsunami of Compute Load
Jorg Lotze and Hicham Lahlou

 

This article gives an overview of the different xVA adjustments, such as CVA, DVA, and FVA, shows how they are typically computed, and outlines where the computational complexities lie. We give recommendations on how to achieve high performance, portability, and scalability for centralised in-house xVA implementations. We show how, by careful software design, we can easily harness, not only the power of multi-core CPUs, but also accelerator co-processors such as graphic processing units (GPUs) and the Intel Xeon Phi.


Pricing Credit Derivatives with Uncertain Default Probabilities: Wilmott Magazine Article
Vivien Brunel 1891 Views

One main problem of credit models, as in stochastic volatility models for instance, is that the range of arbitrage prices of risky bonds and credit derivatives is generally very wide. In this article, we present a model for pricing credit spread options in an environment where the rating transition probabilities are uncertain parameters. Thetransition intensities are assumed to lie between two bounds which can be easily interpreted in the light of the rating agencies' transition matrices. These bounds are a confidence interval of the rating transition intensities. We show that the bounds of arbitrage prices are solutions of a non-linear partial differential equation. In particular, when using realistic values for the rating transition (default) probabilities, the arbitrage range of credit derivatives prices remains narrow.

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