This document summarizes some of the key challenges in computational finance, specifically around valuing and risk managing derivatives. It discusses how derivatives are priced using simple models but notes credit and liquidity risks were not fully accounted for. It then covers the importance of credit valuation adjustments to account for counterparty default. The rest of the document discusses the complexity of implementing these adjustments at a portfolio level with many instruments and counterparties, and the use of GPUs to help with the significant computational requirements. Finally, it outlines some research projects underway to develop more advanced modeling techniques.

1. Challenges in Computational Finance
Drona Kandhai (PhD)
Head of FO Quantitative Analytics – ING Bank
Assistant Professor Computational Finance – UvA CSL

2. Outline
Background
• Derivatives:
• Introduction
• Valuation and Risk
• Challenges after credit and liquidity crisis
• Teams at ING and UvA
Research Projects in progress
Final Thoughts
I will not cover …. !!!!
Funding CostsFunding Costs

3. Derivatives
• A derivative is a financial product whose value depends on the
values of other more basic underlying assets.
• Examples:
 Forward contract on a stock: a contract written today, to buy a stock at
time = T at strike price K.
 Call option on a stock: a contract written today, which gives the holder
the right but not the obligation to buy a stock at time t=T at strike price
K
 Key questions:
 What is the fair premium I should charge?
 How to manage the risks?

4. Derivatives
Market Volume in Notional Outstanding
Trillion = 10^12

5. A Simple Two-State World
• A stock price is currently $20
• In three months it will be e.g. either $22 or $18
Stock Price = $22
Stock Price = $18
Stock price = $20
q
1-q

6. What is the value of a Call Option?
A 3-month call option on the stock has a strike price
of 21.
Stock Price = $22
Option Price = $1
Stock Price = $18
Option Price = $0
Stock price = $20
Option Price=?

7. Setting Up a Riskless Portfolio
• Consider the Portfolio: buy (long)  shares and sell (short) 1 call
option
• Portfolio is riskless when 22– 1 = 18 or  = 0.25
22– 1
18

8. Valuing the Riskless Portfolio and Option
• Risk-Free Rate is 0%
• The riskless portfolio is:
long 0.25 shares
short 1 call option
• The value of the portfolio in 3 months is
22x0.25 – 1 = 4.50
• (No arbitrage) The value of the portfolio today is 4.50
• The value of the shares is 5.000 (= 0.25 x 20 )
• The value of the option is therefore 0.5 (= 5.000 – 4.50 )

9. Summary
• We can mathematically show that the value is the expectation of
the payoff at expiry discounted back to today
• The probabilities are implied by the hedging argument
• Generalize by considering many different scenarios for the
underlying and take averaged value (Monte Carlo Methods or PDE
Solvers)
• Idea has been awarded Nobel price in economics
• Nevertheless we forgot something which had pronounced impact
in the recent credit crisis

10. Credit Valuation Adjustment
• Counterparty credit risk is the risk that a counterparty in a
financial contract will default prior to the expiry of the contract and
will be unable to make future payments.
• Credit value adjustment (CVA) is the difference between the risk-
free portfolio value and the true portfolio market value that takes
into account the possibility of a counterparty’s default. In other
words, CVA is the market value of counterparty credit risk.
• How to value CVA?

11. Consequences…
CVA magnitude depends on
• The probability of default of the counterparty
• The possible exposure in the future (only if it is
positive!)

12. 12
Key Building Block
Expected Positive (Negative) Exposure
Expected Positive Exposure
Our exposure to the counterparty
Exposure of counterparty to us

13. Key Building Block
Expected Positive (Negative) Exposure

14. Portfolio Credit Valuation Adjustment
From Single Instrument to Portfolio
Portfolio of instruments in scope:
 Roughly 50K instruments exposed to
counterparty risk
 All market conventions, netting and
collateral rules
 >30 currencies
 >6000 counterparties
Modelling complexity
 Multi-currency Hybrid Modelling
(IR/Credit/FX) with Monte Carlo (3K
Paths)
 Exposure grid with close to 100
points
IT complexity
 Interfacing with Multiple Systems
 Application Development
Computational Complexity
 For one CVA run with 50K instruments
3.75 billion pricing evaluations
 For a full CVA sensitivity run (> 800 runs)
hundreds of billions of evaluations
 For an HVaR run with 50K instruments
13 million pricing calls

15. Analytics Complexity
• Complex Hybrid Modelling
• Large number of correlated market (IR, FX, Inflation and Commodities) and
credit risk (CDS) factors in one unified framework
• Wrong-Way-Risk modeling where exposure is correlated with credit
• Illiquidity
• Default probabilities are implied from CDS spreads, nevertheless proxy credit
curves for counterparties with illiquid CDS are needed
• Lack for FX, IR and Inflation option quotes (especially for emerging markets)
typically required for model calibration
• Numerical Complexity
• Handling exotic derivatives efficiently is not easy in such a setting
• Due to large number of sensitivities special tricks are needed

16. GPU Computing
Think of your Gaming Device
GPGPU = general-purpose computing on graphics processing units
CPUs
• Optimized for fast access to cached
data
• Control logic for out-of-order and
speculative execution
GPUs
• Embarrassingly parallel
• SIMD (single-instruction multiple-data)

17. 0
20
40
60
80
100
120
CPU - Grid 1 GPU 2 GPUs 32 GPUs
120 min
4 min 2 min 20 sec?
GPU vs CPU Performance
Portfolio CVA of 50k trades
 30x faster on 1 GPU
 60x faster on 2 GPUs

18. The Group@ING
The group@ING consists of
• Quantitative Analysts and Developers
• Model Integrators and GUI/DB Developers
• IT Support Engineers (Application and HPC Grid)
• Strong Joint-Venture between IT engineers and quantitative analysts
Strong interaction with Business and Risk
• Trading, Sales, Market and Credit Risk
Broad Expertise and Experience
• Financial Markets
• Hybrid Modeling (Interest Rates, FX, Credit, Inflation, Commodities)
• Data Analytics
• High Performance Computing
• Software Development

19. Research group at UvA
Close collaboration with
• Industry
• MSc projects (currently 5 are running)
• PhD and other R&D projects
• UvA/CWI/TU Delft (STW funded project 2012-2016)
• ITN Horizon 2020: Big Data in Finance (EU Funded)
• ING Funded PhD position on Advanced Modeling

20. Selected Research Projects

21. • Bermudan swaptions are options on swaps, where the buyer
has a right but not an obligation to enter into a swap
• The option can be exercised on pre-agreed dates before the
swap matures
• Valuation is monte carlo based
• This makes it challenging in CVA context, where we need to
simulate the products MtMs on future market scenarios (which
leads to Nested Monte Carlo).
CVA of Bermudan Swaptions
21
Interest Rate Swap

22. • Regression based approximation for Bermudan swaption Mtms
is one way to avoid nested Monte Carlo (other being PDE based
approach).
• SGBM (Stochastic grid bundling method) (Regression +
clustering)
An efficient approach for Bermudans
22

23. Exposures for Bermudan swaptions
23

24. Other Projects
Network and Information Theory Based Models – dr Sumit Sourabh
Big Data in Finance – Recruitment of PhD Student

25. 25
Final Thoughts
• Innovation in industry does not end with a proof-of-concept
study!!!
• Future is holistic …
• Advanced Analytics:
• Hybrid Pricing & Risk models even for simple plain vanilla derivatives
• Data Analytics (client behaviour, market moves and other non-textual
data)
• Complex system based approach for systemic risk
• High Performance Computing due to vast computational
requirements
• Efficient numerical methods
• Interested: Attend Computational Finance course