mathematics and technology in investment … › ... › qat_gdansk_uni_introduction.pdfmathematics...

Mathematics and Technology in Investment Banking Introduction to Quantitative Analysis

Gdansk University of Technology, December 11, 2019

Adam Lodygowski, PhD Quantitative Strategies and Technology Poland Head Sasha Gituliar, PhD Quantitative Strategies Counterparty Credit Modelling

Public

Quantitative Strategies Technology at Credit Suisse 4

Quantitative Strategies Modelling at Credit Suisse 3

Introduction to Quantitative Analysis and Technology 2

Introduction to Investment Banking and Credit Suisse 1

Agenda

2 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski

Quant Training at Credit Suisse Poland 5

Real-Life Application of Mathematics in Investment Banking 6





Agenda




Introduction to Investment Banking Few Facts

Current world debt is nearly $250 trillion

(3 times the size of global economy) and

belongs to:

– Non-financial companies

– Governments – Households

– Emerging Markets It allows economic actors to spend more

than their incomes would otherwise allow

Problem arise when the debt is excessive and repayments potentially cannot be met

Why global economy needs Investment Banks?


5

More than 530 offices

With over 46,000 employees

In over 50 countries

Private Banking & Wealth Management

and Investment Banking across all major markets

Headquarters: Zurich

– New York is Investment Banking

and Americas Headquarters

– London and Hong Kong are regional

Headquarters

Truly Global Financial Services Firm

4 Regions

Switzerland

1,600+ relationship

managers

200+ branches

Asia Pacific

24 offices

12 countries

Americas

42 offices

14 countries

Europe, Middle East & Africa

UK headquarters

75 offices in 30 countries

December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski

6

Credit Suisse has had a presence in Wroclaw since 2007

and in Warsaw since 2017

Credit Suisse Poland is now one of our largest offices in

Europe, employing over 5,000 people

We are located in the heart of Wroclaw’s central business district

in The Green Day and Grunwaldzki Centre buildings

We are located in central Warsaw in Atrium 2 building

Both locations provide vital support to our businesses around

the world and also provides a wide range of global support

services, including: – Accounting Services

– Human Resources

– Information Technology

– Legal and Compliance

– Marketing

– Communications

– Operations

Credit Suisse in Poland

Wroclaw – Grunwaldzki Center

Wroclaw – Green Day

Warsaw – Atrium 2

December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski





Agenda




Quantitative Strategies and Technology at Credit Suisse

Trading

Quant Strats

Quant Technology & Data

IT

25% now in Wroclaw

Covering all business areas in Fixed Income

Credit, Emerging Markets, Foreign Exchange,

Interest Rate Products, eTrading, XVA and

Regulatory

– Quant Strats Modeling for Trading Models and analytics to help the business

– Quant Technology & Data

Infrastructure, tools, data quality for developed

analytics

Part of the Investment Bank

Established in 1990

ca 500 people globally

– primarily London, New York, and Wroclaw


Type of quants

– Front office quant

– Library quantitative analysis

– Algorithmic trading (statistical arbitrage)

– Risk management (VaR, stress testing, economic capital) – Innovation

– Model validation – Quantitative developer

Area of expertise

– Numerical approximations to solve PDE – Stochastic calculus (Ito integral) – Spline interpolation (interpolate spot and forwards interests, curves and volatility)

– Desktop and web-based application development for financial industry – Computer science for large versioning environments

– Code base development, maintenance, architecture design

– Releasing software containing financial and technological components to end users

Quantitative Analyst Concept Who We Are and What We Do






Agenda




Quantitative Strategies Modelling Mathematical Modelling for Pricing Derivatives

Models and analytics

– To help the business

Teams in London and New York

– Sit close to the business users

The Wroclaw team provides strong support

to these global teams and with continuously increasing expertise becomes more independent stakeholder – Extending existing models to cover

new financial products – Streamlining models

– Cross cluster independent projects – Integrating new models into risk systems – Analysis and performance improvements – Direct front office support

Area of expertise

– Finite difference method to solve PDE – Monte Carlo Method so solve PDE – Stochastic calculus (Ito integral) – Spline interpolation (interpolate spot and

forwards interests, curves and volatility)

Use C++ and F#

(functional programming language)


Quantitative Strategies Modelling Very Simple Example

Calculating PV where:

r is interest rate for each interest capitalization period

n is number of those capitalizations (expressed in years)

FV = PV(1 + r)n

𝑟 =

𝐹𝑉

𝑃𝑉

52

− 1






FV = PV(1 + r)n

𝑟 =

𝐹𝑉

𝑃𝑉

52

− 1

Take a 100 PLN loan („week till payday”), paying back 109 PLN

How much would I have to pay back in 3 years time, considering I would take next loan to repay the previous one?






FV = PV(1 + r)n

𝑟 =

𝐹𝑉

𝑃𝑉

52

− 1

Take a 100 PLN loan („week till payday”), paying back 109 PLN

How much would I have to pay back in 3 years time, considering I would take next loan to repay the previous one?

Considering 52 weeks in year:

Interest rate: 8734.42%

Total payoff given 3 years of a loan: 68,979,977 PLN !!!

𝑟𝑎 =109

100

52

− 1 ≅ 87.3442


Quantitative Strategies Modelling Forward Contract

Provides financial solutions for individuals, corporations, and governments

Many of these are bespoke products that are not liquidly traded in the market

Current EUR/PLN exchange rate is 4.301

Problem:

– The company does not know what the exchange rate will be in one year

– How much will they have in PLN to pay employees?

Extra risk for the company

Possible solutions:

– Lock in exchange of 4.30 now – Offer an exchange rate of 4.30 or better – Offer them the average monthly exchange

rate over the coming year

Example

In one year

PLN EUR 100 m

1 As of 22/11/2019 close


Quantitative Strategies Modelling Forward Contract

These solutions offer a lot of value for the client, allowing them to concentrate on their core business

– How much should we charge them?

– How can we limit our own exposure?

This is where Quant Strats comes in… Develop mathematical models for the exchange rate

SdWSdtdS T

rT VeV Ε0

02

12

22

rVS

VrS

S

VS

t

V

These models allow us to price any trades – may require a lot of calculations

Work out how we should manage the risks on this trade

Can we enter into other contracts to offset some of the risk – hedging






Agenda




Quantitative Technology & Data

Quantitative Analysis library is a project started in 90s

Millions of line of code in C++ and F#

Uses every part of Computer Science – from algorithms and data structures to software engineering

of large projects

For analytics library - developing a it rather than service or application has very strong implications

There are different models of quant development – from very strong separation between modelling

and development to one man band. There are no rights or wrongs, we are placed somewhere in the

middle

// F# example – what does this output?

let rec fac n = if n <= 1 then 1 else n * fac (n-1)

let square (f : int int) n = f(n) * f(n)

printfn “Output = %d” (square fac 4)


Continuous Integration for the Models

P4

Build

Build

UT

Test

Quick

Fast

System Test

Hard

Heavy

Asynchronous feedback pipeline

Private Cloud

Local Cloud


Risk Engine Frameworks

Risk (Model or FDM)

Scenarios (Diff Markets)

PV (Model + Data)

Models

Market Modelling Data

Facade and lifecycle managment for financial models

Provides consistent quantitative calculations across thebank


Contin

uous

Deliv

ery

To

olc

hain

Audit DB Monitoring

Pricing Frontends (Function as a Service)

Quant

Dev Ops

Cloud Local Runner

Cloud Native API

MyApp: MyServices

Press a button

Source Control DB

Build Automation

Test Automation

Sign-off Automation

Deploy Automation

Cloud Native

Runtime

Expert Support

(audits & traces)






Agenda




Quant Scholarship Program at Credit Suisse

Quant Summer Institute at Credit Suisse

CRO Graduate Program at Credit Suisse

Full time employment

Contact information:

– Adam Lodygowski [email protected]

Quant Training at Credit Suisse Poland


mailto:[email protected]



Questions and Answers

26

Appendix

27

Submission deadline: 10th of January 2020 (optionally you may submit the answer with your CV)

Two participants with correct answers will be selected to receive the award*

Award: fully sponsored one day trip to Credit-Suisse Office in Wroclaw *in case more candidates submit the correct answers the candidates with be drawn

Question 1

In the land of Cool, everybody follows a pretty awesome philosophy called Awesomism. One day, a philosopher comes up with a radical new philosophy called Radicalism. He makes it his mission to convert the entire population of Cool to this new philosophy. He’s very good at his job – every Awesome person he meets converts to Radicalism. Unfortunately he’s a little too fanatical – whenever he encounters somebody that is already Radical, half of the time they’ll convert back to Awesomism. In the long term, what percentage of the population is Radical?

Question 2

Suppose that you are building the regression equation between the univariate variable Y and the univariate variable X, of the form Y = a0 + a1 _ X + error (this error is i.i.d.) You are not given any data, but you are told that: • The sample covariance between X and Y is 3 • The sample variance of Y is 7 • the variance of X is 1.5 • the sample mean of Y is 10 • the sample mean of X is 20. What are the estimated values of a0 and a1?

Question 3

Consider a one-dimensional random walk starting at the origin. At each step, it moves +1 or -1 with equal probability. What is the probability it hits 9 before it hits -1?

Open Questions Please submit answers: [email protected]


mathematics and technology in investment … › ... › qat_gdansk_uni_introduction.pdfmathematics...

Documents