Constructing an Implied Volatility Model For Counterparty Credit Risk

Dr Chris Cormack

Introduction

Building an implied volatility model for traded counterparty credit risk is fraught with challenges, capturing the combined dynamics of the complete surface from 1 day to over 3 years, capturing variations in the skew and smile for all moneyness values possess a real challenge, especially when strict arbitrage constraints must be applied.

Although only a few organisations require such models due either due to complex volatility products of significant volatility exposures within their counterparty exposures capturing the dynamic of implied volatility coupled to a stochastic spot process can provide notable reductions in RWA.

Current Practice

There are a wide range of practices amongst banks, ranging from constant volatility, non-arbitrage free adjustments of implied vol, the use of stochastic volatility models such as Heston for simplicity, to some that have adopted cut-down full surface models.

Clearly those that are using fixed vols or non-arbitrage free volatility surfaces there are challenges in ensuring a coherent set of dynamics for the model and potential problems in model pricing issues due to static arbitrage across the surface.

For those using traditional stochastic volatility models like Heston, creates a challenge on being able to coherently reproduce the whole surface and being able to convert the model volatility to an implied volatility for pricing.

For those using low dimensional models for the surface, this can create issues of incomplete modelling of regions on the surface, typically away from ATM and unrealistic dynamics of the wings.

Quant Foundry Solution

At the Quant Foundry we have developed a sophisticated but low dimensional class of arbitrage free models of equity implied volatility surfaces that uses a lower dimensional process that the current full surface models used in practice.

The model can capture a not only the term structure of the ATM volatilities, but also a term structure dynamic of skew and surface convexity whilst ensuring the surface is arbitrage free.

The model is well suited for traded counterparty credit risk, market risk modelling and xVA , providing pricing coverage for the majority of Equity Derivatives.

Result Highlights

As a demonstration of the models’ capabilities we show the results from a model simulation from of a volatility surface from 1 Month to 3 Years for a moneyness range from 25% to 175% with the ATMF volatility. The data in blue is shown with the 99^th and 1^st percentiles for a 1-year simulation time horizon.

The model has a very good coverage over a wide number of expiries and moneyness values, offering superior coverage of volatilities compared to conventional implied volatility modelling techniques currently used in practice.

Quant Foundry

Dr Chris Cormack and David K Kelly formed Quant Foundry in 2018 with the understanding that our success depended on our ability to attract and retain talent.

Through our unique control framework, each senior quant has access to our collaborative and multi-sector network of problem solvers that support and challenge solution choices as well as a quality assurance “check-in, deliver, check-out” framework that enforces consistent, high-quality delivery. 

Rather than have a costly “bench”, our Quant Labs division runs several research-based and highly creative initiatives inside and outside of finance where our senior practitioners expand their knowledge base as well as supervising our junior PhD talent pool. Where all members of the Quant Foundry can contribute new applications.