CCR KVA Relief Through CVA, Homotopy Analysis for SABR and XVA, R for ML: Self Organising Maps for Risk Analysis

The latest research and articles from the pages of Wilmott Magazine's January 2019 Issue

In ‘CCR KVA Relief through CVA: a Regression-based Monte Carlo Approach’, published in the January 2019 issue of Wilmott Magazine,  Christoph M. Puetter, Stefano Renzitti, Allan Cowan present and examine, by example of a USD interest rate swap and a EUR/USD cross-currency basis swap, a regression-based Monte Carlo approach to counterparty credit default risk (CCR) capital and CCR capital valuation adjustment (KVA) calculations [assuming the standardized approach to counterparty credit risk for exposure-at-default (SA-CCR EAD) and the internal ratings-based (IRB) approach for CCR risk weights].

This approach allows the authors to incorporate the capital lowering effect of credit valuation adjustment (CVA) in an efficient manner, without having to resort to lengthy nested Monte Carlo simulations.

The authors find that the regression-based Monte Carlo approach works well in most situations.

In other situations, the accuracy of the approach is sensitively controlled by the choice of explanatory variables. The authors discuss in detail the conditions and underlying dynamics under which this happens.

In computing and presenting a selection of numerical examples, the authors also explore the impact of dynamic CCR risk weights on CCR KVA, and compare regression-based CCR KVA results with CCR KVA results from nested Monte Carlo, alternative frequently used CCR KVA simplifications, and standardized CVA KVA.

In the same issue ‘Homotopy analysis method applied to SABR and XVA’ by Takayuki Sakuma, observes that the evaluation of SABR models in finance using asymptotic formulas for implied volatilities is fast and widely used but becomes less accurate and exhibits negative probability distribution values around zero strikes for long maturities. In addition, an alternative version for more accurate valuation exists but involves numerical integration. In this paper, the author applies the homotopy analysis method (HAM) to derive approximated option prices under a SABR model. This scheme is simple, and numerical examples demonstrate that the derived price can be evaluated easily and gives a good approximation with a computational cost that is only several times heavier than that of the Black-Scholes model. The author also discusses the application of HAM to XVA evaluation.

In Claus Huber’s ‘R Tutorial on Machine Learning: How to Visualise Option-like Hedge Fund Returns for Risk Analysis’ Non-linearity in financial market returns is commonplace and in particular in hedge fund returns (Fung/Hsieh (2001), Mitchell/Pulvino (2001)). Hedge Funds are known to generate option-like returns based on the products they trade as well as their trading strategies. This tutorial describes how Kohonen’s (2001) Self-Organising Map (SOM), a method of Machine Learning, can help to analyse non-linearity in returns. Huber focuses on simple examples that help the reader to understand where non-linear hedge returns come from, why linear correlation analysis is inappropriate and how SOM can help to visualise non-linear returns to enhance risk analysis. R code and step-by-step instructions enable the reader to reproduce the creation of the SOM. Readers are encouraged to change parameters and study the impacts on results.

This issue Paul Wilmott and David Orrell proclaim that there are ‘No Laws, Only Toys’

“Quantitative finance does not have any fundamental laws.” They write, “There’s no such thing as conservation, for example. If a share price falls 50% in one day, then half the company’s value has just disappeared. If there are no laws, then we might try to rely on statistics. We can still build up a solid model. But if the statistics are not stable, then our model might be limited in accuracy. That’s finance.” But where does this leave the Quant who “… sees an idea like the efficient markets hypothesis and thinks he’s back in the quadrangle with Dirac.”? The truth is Quant Finance could learn much from other disciplines (like Mathematical Biology) that revel in the fact that you don’t need perfect models to be a science, and still produce useful insights in to mechanisms and behaviours despite the scarcity of applicable, reliable physical laws in the models. “Embrace the fact that the models are toy,” the authors suggest, “and learn to work within any limitations. Focus more attention on measuring and managing resulting model risk, and less time on complicated new products.”

Aaron Brown draws our attention to, erm, ‘Kelly Attention’, Aaron writes “The hardest part about being a risk manager is choosing how to allocate your attention. No one can possibly understand all potential issues affecting an entity in depth. There will be problems caused by issues that you neglected to study. There will be problems caused by unexpected aspects of issues you did study. If you worry too much about the former, you won’t have sufficient attention to devote to in-depth understanding of the obvious first-rank risk issues. If you worry too much about the latter, you will be blindsided.”

The logic behind the Kelly criterion gives a great simplification that converts the risk manager’s “attention problem” from impossible to just very difficult.

Espen Gaarder Haug continues his journey in to the “Philosophy of Randomness” with a look at “Time in Relation to Uncertainty” and finds that the infinitesimally small intervals of Planck Time might hold some useful food for thought in finance.

‘Kelly Gone Bad’ finds Rolf Poulsen observing that there “… is a considerable literature on the statistical modelling of sports results. Many papers use bookmakers’ odds to test if their model can generate profitable betting strategies. While I find this fundamentally very sound, the strategies considered most often bet fixed amounts. From the betting or finance literature we know that it is optimal to behave in a way that reflects risk, expected reward, and current wealth. Specifically, there are many arguments for using the Kelly-strategy, also known as the growth optimal portfolio. However, that bright idea never seemed to work very well on data for me; marginally profitable strategies were turned into really poorly behaving ones. In this column I will tell you why.”

Uwe Wystup looks at ‘FX Greeks’ covering the different types of Greeks commonly used on the FX Options context. “In FX, Greeks can be confusing,” Wystup writes, “because they depend on the quotation of the currency pair as well as the currency in which they are calculated. Furthermore, premium can be included or excluded, smile-effect can be included or not included, and numerical approximations may further add to the confusion. We will now cover all the possibilities step by step.”

Leonard MacLean and William T. Ziemba examine ‘The Efficiency of NFL Betting Markets’  considering odds and available information and whether the odds reflect all relevant information. The information the authors access is from the site 538, which reports NFL team strength ratings prior to a game. MacLean and Ziemba check to find if the odds and spreads based on that information are fair.