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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