From Physics to Financial Engineering - Institute for Structure and ...

**Financial** **Engineering**

Boris Skorodumov

Junior Seminar

September 8, 2010

Biography

Academics

B.S Moscow **Engineering** **Physics** **Institute**, Moscow, Russia, 2002

Focus : Applied Mathematical **Physics**

Ph.D Nuclear **Physics**, University of Notre Dame, Indiana, 2007

Focus : **Structure** of Light Exotic Nuclei

M.S Mathematical Finance, Columbia University, New York, New York, 2008

Focus : S**to**chastic Mathematics, Probability, **Financial** Mathematics

**Financial** Industry

Mitsui & Co, 2008 - 2009; http://www.mitsui.com

Focus : Commodities (Natural Gas **and** Oil Trading)

Platts, 2009 - 2010; http://platts.com

Focus : Commodities (Natural Gas, Model Analytics)

NumeriX, 2010 – Present; http://numerix.com

Focus : Equities, Foreign Exchange (FX), Commodities

I model **and** price complex exotic deals related **to** equities, fx **and** commodities.

I also developing new financial models **for** different financial products.

Overview

1. Quantitative Finance

2. Derivatives. Example of Forward FX Contract. Call/Put **and** exotics

3. **Financial** **Engineering**.

Topics in Mathematics, Finance, Programming.

FE Schools **and** requirements

4. Binomial Tree. How **to** price Call option

5. Links **and** Conclusions

Definitions

• Quantitative Finance

• **Financial** **Engineering**

• Computational Finance

• Mathematical Finance

Individuals are known as “Quants”In financial world

**Engineering**

Mathematics

Computer Science

**Physics**

Finance

Economics

Example of simple derivative

Company A would like **to** sell parts of airplane **to** company B. Company A located in USA **and** company B in Engl**and**.

Company B will pay one million pounds in 6 months from now **for** parts **to** company A.

USA

Parts

Engl**and**

A

£1,000,000

B

Transaction will occur

GBM/USD = 1.65 GBM/USD = ?

**to**day

6 month

Today : £ 1,000,000 = $1,650,000

**Financial** Notation :

GBM/USD – Number of USD per 1 GBM

GBP/USD Description

Bloomberg System : http://bloomberg.com

His**to**rical Exchange Rate

$ Amount

Futures scenarios

1,850,000.00

1,800,000.00

1,750,000.00

1,700,000.00

1,650,000.00

1,600,000.00

1,550,000.00

1,500,000.00

1,450,000.00

1,400,000.00

1,350,000.00

1.5 1.55 1.6 1.65 1.7 1.75 1.8

Exchange rate (GBP/USD)

Unhedged

Hedged

GBP/USD GBP USD Difference

1.5 1,000,000.00 1,500,000.00 (150,000.00)

1.55 1,000,000.00 1,550,000.00 (100,000.00)

1.6 1,000,000.00 1,600,000.00 (50,000.00)

1.65 1,000,000.00 1,650,000.00 0.00

1.7 1,000,000.00 1,700,000.00 50,000.00

1.75 1,000,000.00 1,750,000.00 100,000.00

1.8 1,000,000.00 1,800,000.00 150,000.00

Example of simple derivative : Forward Contract

Bank

£1,000,000

A

parts

B

$1,000,000*FX

£1,000,000

Bank View :

Buy 1,000,000 of GBP

Sell 1,000,000 GBP * 1.65 USD/GBP = 1,650,000 USD

P&L

Bank

Forward Contract

F(T) = S(T) – K

100,000

-100,000

1.55 1.65 1.75

S(T)

K=1.65

K – delivery price (1.65)

S(T) – exchange rate at expiration T

6M Forward Contract on GBPUSD exchange rate

Simple Derivatives : Call, Put, Forward

Payoff

Call Option

Payoff

Put Option

0.1

0.1

-0.1

1.55 1.65 1.75 S(T)

-0.1

1.55 1.65 1.75 S(T)

C(T) = Max(S(T)-K,0)

P(T) = Max(K-S(T),0)

Payoff

C(T) – P(T)

Payoff

P(T) – C(T)

Forward

0.1

0.1

-0.1

1.55 1.65 1.75 S(T)

-0.1

1.55 1.65 1.75 S(T)

Arbitrary Payoff

Payoff

Payoff

Payoff

S(T)

S(T)

S(T)

Derivatives **and** asset classes

There are two groups of derivatives contracts which are distinguished by the way they are traded in the market

•Over-the-counter derivatives (OTC)

•Exchange-traded derivatives (ETD)

Three major classes of derivatives:

•Futures/Forwards

•Options

•Swaps

Five major classes of underlying asset:

•Interest rate derivatives

•Foreign exchange derivatives

•Equity derivatives

•Credit Derivatives

•Commodity derivatives

•Inflation derivatives

(Rates)

(FX)

(Equities)

(Credit)

(Commodities)

(Inflation)

Mathematics

**Financial** Mathematics comprises the branches of different approaches **for** pricing financial

derivatives

S**to**chastic Calculus is a branch of mathematics that operates on s**to**chastic processes. One

of the example of s**to**chastic process is well know Brownian motion

Numerical Methods is a set of techniques which allow so solve numerically differential equations

Monte Carlo Simulations is a technique which allow **to** model complex market behaviors

using simulation **for** r**and**om processes

Statistical Analysis comprises of set of statistical techniques **to** analyze financial data

Programming

C++ is a main programming language employed **for** the mathematical calculations In quantitative finance

Java is also used **for** mathematical calculations but in extent as C++. Another area of usage is gui interfaces **and**

real time data processing

C# (“C Sharp”) is a product of Microsoft. It is used whenever code developed under windows system. It is mostly

used **for** GUI interfaces, databases manipulations, web services, web application.

Python, Perl is a scripting languages which is used **for** parsing purposes. They are also used as a front end

**for** C++ libraries.

Matlab, Mathematica, R is a modeling systems which is used **for** testing purposes of models.

Quantlib http://quantlib.org

Books

Selected Books

Rotman School of Management, Canada

http://www.rotman.u**to**ron**to**.ca/~hull

Professor Paul Glasserman,

Columbia University

http://www2.gsb.columbia.edu/

faculty/pglasserman/Other

Carnegie Mellon University

http://www.math.cmu.edu/~ccf/docs/Faculty/shreve.htm /

Daniel Duffy

http://www.datasimfinancial.com

**Financial** **Engineering** Programs

Rank

School

Program

Duration

•1 - 5

•1 - 5

•1 - 5

•1 - 5

•1 - 5

•Carnegie Mellon University

•Columbia University

•Prince**to**n University

•Stan**for**d University

•University of Chicago

•MS, Computational Finance

•MS, **Financial** **Engineering**

•MS, Finance

•MS, **Financial** Mathematics

•MS, **Financial** Mathematics

•1.5 years

•1 year

•2 years

•1 year

•1 year

•6 - 10

•6 - 10

•6 - 10

•6 - 10

•6 - 10

•Baruch College, New York

•Columbia University

•Cornell University

•New York University

•University of Cali**for**nia at

Berkley

•MS, **Financial** **Engineering**

•MA, Mathematics of Finance

•MEng, FE Concentration

•MS, Mathematics in Finance

•MS, **Financial** **Engineering**

•1.5 years

•1 year

•1.5 years

•1.5 years

•1 year

2009 Quant Network Ranking

http://www.quantnet.com/**for**um/showthread.php?t=5415

What is common **for** all FE programs

About 1.5years of study ( ~30 credits)

The MFE requires only one year of study, which makes it attractive **to** students with

strong quantitative skills **and** focused career interests.

Quality Instruction

Competitive Admission

Tailored Curriculum

Faculty is comprised of distinguished finance instruc**to**rs. Faculty per**for**ms preeminent

research in quantitative finance, research that feeds directly in**to** the math finance

curriculum

Program receiving a very large number of applications ~ 1000. The ~50 students are

usually accepted. The following are required: TOEFL, GRE/GMAT, Recommendations

Courses are designed exclusively **for** FE students, **and** are seamlessly integrated

with one another. This cooperation between course material allows the mathematical,

statistical, **and** computer science methods **to** be integrated with the theoretical

framework **and** institutional settings in which they are applied.

**Financial** Seminars

Career Planning

MFE students are encouraged **to** attend weekly discussions held by finance

practitioners.

A highly dedicated MFE Program staff works **to** maximize the job-seeking skills of

students **and** employs an extensive network of contacts **to** secure both internships **and**

career positions

Binomial Tree

H

HH

1/2

1/4

1/2

1/4

1/8

3/8

HHH

HHT,THH, HTH

HT, TH

1/2

1/2

3/8

TTH,HTT,THT

T

TT

1/2

1/4

1/2

n

k nk 3

1 1

P( k)

p (1 p)

k

2

4 2

3

8

1/4

1/8

TTT

S

p

1 - p

uS

dS

u 2 S

udS

d 2 S

S

uS

dS

u 2 S

udS

d 2 S

u 3 S

u 2 dS

ud 2 S

d 3 S

u n S

u k d n-k S

d n S

0

Δt

2Δt 3Δt T = nΔt

Binomial Tree

p = (exp(r*Δt) – d)/(u – d)

p

uS

u = exp(σ*sqrt(Δt))

How **to** choose u, d, p ?

d = exp(-σ*sqrt(Δt))

S

0

1 - p

Δt

dS

σ - volatility of the

log s**to**ck returns

r - risk neutral

interest rate

S**to**ck

p

uS

Option

p

C u

Money

p

$1*exp(Δt*r)

S

1 - p

dS

C

1 - p

C d

$1

1 - p

$1*exp(Δt*r)

0

Δt

0

Δt

0

Δt

t=0 : C = x*S + y*$1

t = Δt, up :

t = Δt, down :

C u = x*u*S + y*exp(Δt*r)

C d = x*d*S + y*exp(Δt*r)

Binomial Tree

C = exp(-Δt*r)*(p*C u + (1-p)*C d

Payoff

S(T)

C uu

C uuu

max(u n S – K,0)

C u

C

C ud

C uud

C u = exp(-Δt*r)*(p*C uu + (1-p)*C ud

Δt 2Δt T = nΔt

max(u k d n-k S, 0)

C udd

C d

C dd

C ddd

max(d n S – K ,0)

0

3Δt

Process:

• Build binomial tree **for** underling asset

• Build backward pricing **for** the option

Call price

Binomial Tree

sig 30%

r 5%

S 50

K 50

T 0.1

n 10

u 1.030455

d 0.970446

p 0.500835

1-p 0.499165

Price **and** delta **for** a T=0.05 maturity call option

9

8

7

6

5

4

3

2

1

0

42 44 46 48 50 52 54 56 58 60

S**to**ck price

Call

Links

WILMOTT Website

http://www.wilmott.com/

Global Derivatives

http://www.global-derivatives.com/

International Association of **Financial** Engineers

http://www.iafe.org/html/

Thank You