Challenges in Computational Finance

Drona Kandhai (PhD) Head of FO Quantitative Analytics – ING BankAssistant Professor Computational Finance – UvA CSL

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

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?

DerivativesMarket Volume in Notional Outstanding

Trillion = 10^12

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

What is the value of a Call Option?

A 3-month call option on the stock has a strike price of 21.

Stock Price = $22Option Price = $1

Stock Price = $18Option Price = $0

Stock price = $20Option Price=?

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

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Valuing the Riskless Portfolio and Option

• Risk-Free Rate is 0%• The riskless portfolio is:

long 0.25 sharesshort 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 )

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

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?

Consequences…

CVA magnitude depends on

• The probability of default of the counterparty• The possible exposure in the future (only if it is

positive!)

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Key Building BlockExpected Positive (Negative) ExposureExpected Positive Exposure

Our exposure to the counterparty

Exposure of counterparty to us

Key Building BlockExpected Positive (Negative) Exposure

Portfolio Credit Valuation AdjustmentFrom 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 counterpartiesModelling 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

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

GPU ComputingThink 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)

CPU - Grid 1 GPU 2 GPUs 32 GPUs0

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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

The Group@INGThe 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

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

Selected Research Projects

• 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

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Interest Rate Swap

• 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

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Exposures for Bermudan swaptions

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Other Projects

Network and Information Theory Based Models – dr Sumit Sourabh

Big Data in Finance – Recruitment of PhD Student

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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