Potential Future Exposure and Collateral Modelling of the Trading Book Using NVIDIA GPUs
19 March 2015
斜谷
GPU Technology Conference 2015
Grigorios Papamanousakis
Quantitative Strategist, Investment Solutions
Aberdeen Ast Management
Jinzhe Yang Grzegorz Kozikowski Quantitative Rearcher, LDI Rearcher
Aberdeen Ast Management University of Manchester
Contents
•PFE Modelling explained
•Cash vs. No-Cash Collateral – The impact of haircut on the valuation •GPU implementation
•Q & A
Consider the problem of calculating the potential Future Collateral Requirements of a large derivative book for a global ast manager
•Purpo: Provide a probabilistic approach of what may be the collateral requirements, on various granularity levels (fund level, counterparty level, division level, company level, etc.) and different time horizons, of clients portfolio
西晋•Additional information could be extracted as well. Collateral decomposition (Cash Collateral, Gov. Bonds, HY bonds, etc.), counterparty exposure, etc. •Typically the portfolio will include interest rate swaps, swaptions, inflation swaps, cross currency swaps, equity options, CDSs, etc.
Sketching the problem
Wor Ca Scenario
头型图片
Time Horizon
Collateral Requirement
Fund level
Division level
Company level
90% 1w 1m 1y … … £60mln … … £45mln … … £40mln 70%
地菜煮鸡蛋1w 1m 1y … … £30mln … … £23mln … … £20mln Average ca
1w
1m
自我欣赏
1y
… …
讴歌拼音
£18mln
… …
£12mln
平均成绩
… … £10mln
Basic Definitions
•Potential Future Exposure (PFE) is defined as the maximum expected
credit exposure over a specified period of time calculated at some level of confidence. PFE is a measure of counterparty credit risk.
•Expected Exposure(EE) is defined as the average exposure on a future date
•Credit Valuation Adjustment(CVA) is an adjustment to the price of a derivative to take into account counterparty credit risk.
•Collateral can be considered any type of valuable liquid property that is pledged by the recipient as curity against credit risk.
PFE Modelling Explained
胡萝卜怎么画
What do we need to built a ‘standard market’ PFE Model?
•A consistent simulation framework to project forward in time the interest rate curves. This will typically have 100-120 time-steps and around 100k -1mln scenarios
•Multiple stochastic process to simulate the FX exposure for every different currency in the portfolio, aligned with the time steps and the number of simulations of the interest rate scenarios. The same idea applies for the inflation rates but with less time steps
•Correlate all the Brownian motions calibrating on the market data and u the Cholesky decomposition to form multivariate normal random variables and project forward in time on every scenario
•Re-evaluate every position, on every time step, for every scenario and aggregate per netting t to calculate the Expected Exposure - EE
•Calculate the collateral changes bad on the CSA agreement with every counterparty and available collateral on our pool
