Financial Engineering

Transcription

1 Financial Engineering Boris Skorodumov Junior Seminar September 8, 2010

2 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, ; Focus : Commodities (Natural Gas and Oil Trading) Platts, ; Focus : Commodities (Natural Gas, Model Analytics) NumeriX, 2010 Present; 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.

3 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

4 Definitions Quantitative Finance Financial Engineering Computational Finance Mathematical Finance Individuals are known as Quants In financial world Engineering Mathematics Computer Science Physics Finance Economics

5 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

6 GBP/USD Description Bloomberg System :

7 Historical Exchange Rate

8 $ Amount Futures scenarios 1,850, ,800, ,750, ,700, ,650, ,600, ,550, ,500, ,450, ,400, ,350, Exchange rate (GBP/USD) Unhedged Hedged GBP/USD GBP USD Difference 1.5 1,000, ,500, (150,000.00) ,000, ,550, (100,000.00) 1.6 1,000, ,600, (50,000.00) ,000, ,650, ,000, ,700, , ,000, ,750, , ,000, ,800, ,000.00

9 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, , S(T) K=1.65 K delivery price (1.65) S(T) exchange rate at expiration T

10 6M Forward Contract on GBPUSD exchange rate

11 Simple Derivatives : Call, Put, Forward Payoff Call Option Payoff Put Option S(T) 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 S(T) S(T)

12 Arbitrary Payoff Payoff Payoff Payoff S(T) S(T) S(T)

13 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)

14 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

15 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

16 Books

17 Selected Books Rotman School of Management, Canada Professor Paul Glasserman, Columbia University faculty/pglasserman/other Carnegie Mellon University / Daniel Duffy

18 Financial Engineering Programs Rank School Program Duration 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 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

19 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 ~ 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

20 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 n k P( k) p (1 p) k /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

21 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 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)

22 Binomial Tree C = exp(-δt*r)*(p*c u + (1-p)*C d Payoff S(T) C u = exp(-δt*r)*(p*c uu + (1-p)*C ud C uu C uuu max(u n S K,0) C u C C ud C uud max(u k d n-k S, 0) C udd C d C dd C ddd max(d n S K,0) 0 Δt 2Δt 3Δt T = nδt Process: Build binomial tree for underling asset Build backward pricing for the option

23 Call price Binomial Tree sig 30% r 5% S 50 K 50 T 0.1 n 10 u d p p Price and delta for a T=0.05 maturity call option Stock price Call

24 Links WILMOTT Website Global Derivatives International Association of Financial Engineers

25 Thank You