Mathematics and Technology in Investment … › ... › QAT_Gdansk_Uni_Introduction.pdfMathematics...
Transcript of 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
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
3 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
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?
4 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
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
7 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
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
8 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
9 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
10 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
11 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
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)
12 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
13 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
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?
14 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
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
15 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
16 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
17 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
18 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
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)
19 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
Continuous Integration for the Models
P4
Build
Build
UT
Test
Quick
Fast
System Test
Hard
Heavy
Asynchronous feedback pipeline
Private Cloud
Local Cloud
20 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
21 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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)
22 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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
23 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
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
24 December 9, 2019 Introduction to Quantitative Analysis, Adam Lodygowski
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]