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

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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 : Stochastic 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 England.

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

USA

Parts

England

A

£1,000,000

B

Transaction will occur

GBM/USD = 1.65 GBM/USD = ?

today

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


Historical 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

Stochastic Calculus is a branch of mathematics that operates on stochastic processes. One

of the example of stochastic 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 random 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.utoronto.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

•Princeton University

•Stanford 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 California 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/forum/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 instructors. Faculty performs preeminent

research in quantitative finance, research that feeds directly into 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 stock returns

r - risk neutral

interest rate

Stock

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

Stock 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

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