1

REVISED COURSES OF STUDY

M.A./M.SC. IN

COMPUTATIONAL FINANCE

(2012-13)

UTKAL UNIVERSITY BHUBANESWAR-751004

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M.A/ M.SC IN COMPUTATIONAL FINANCE

Regulations:

1. A candidate seeking admission to this programme should have passed Bachelor's

degree with mathematics/Statistics as a subject.

2. The duration of the programme is two years consisting of six terms. Ordinarily the

first and 4th term examinations shall be held in October, second and fifth term

examinations shall be held in the month of January and third and sixth term

examinations shall be held in April.

3. The programme shall have course credit system with internal valuation.

4. A student who has been admitted into this programme can register in a term

examination if he has obtained 75% (subject to a condonation of 15% in case of

ailment) of attendance in the theory and a practical class of that term and pays the

required fees of the University.

5. Each term examination shall consist of two parts: mid term tests and end term

examination having weightage of 30% and 70% respectively for each course.

6. In order to pass a course a candidate has to secure at least 5 or above grade points

in 10 points scale.

7. For passing a term examination a candidate must pass in each course of that term.

8. If a candidate passes all the term examinations he/she shall be declared to have

passed the M.A/M.Sc. in computational Finance.

i. In first class if he /she secures a total grade points average 6.5

or above.

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ii. In second class if he/she secures 5 or more but less that 6.5 of

grade point average.

Total grade point average sum of credit times grade point obtained divided by

sum of credit. ( cisi / ci) where ci = course credit, si = grade point obtained.

9. If a candidate fails in any course (or courses) in any term examination he /she has

to appear the end term examination for that course (or courses) only whenever the

said term examination is held. Passing the said term examination is governed by

regulation 8 and 9 above.

10. If a candidate in the 6th term examination fails to submit the Project Report/

Dissertation by the date fixed for the submission of Project Report/ Dissertation or

if his/her Project Report or Dissertation is not found suitable by the examiners

then he/she shall be allowed to submit the Project Report/ Dissertation after three

months of that year and he/she will be admitted into a special sixth term

examination of that year. If a candidate completes all requirements except two

courses, he may be allowed to appear for a special examination within three

months after the sixth term examination.

11. A candidate who has passed a term examination and wants to improve the results

may appear only once for a maximum of three courses of that term examination

within a period of one year of passing the said term examination. The higher of

the grade points secured shall be taken into consideration for determining the

result.

12. The candidate has to pass all the term examinations within four academic years

from the date of admission failing which his admission to the course will be

cancelled.

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COURSE STRUCTURE

First Year

TERM-1

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

111 Statistics and Probability-I 3 0 3

112 Mathematical Foundation 4 0 4

113 Microeconomic Theory 3 0 3

114 Financial Instruments, Markets and

Institutions

3 0 3

115 Accounting for Decision Making 3 0 3

116 Programming in C++ 2 4 4

TOTAL 18 4 20

TERM-2

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

121 Statistics and Probability-II 3 0 3

122 Corporate Finance 4 0 4

123 Portfolio Theory and Investment Analysis 3 0 3

124 Financial Derivatives 3 0 3

125 Financial Modeling Using Excel 0 4 2

126 C++ Design Patterns for Financial

Derivatives

0 4 2

TOTAL 13 08 17

5

TERM-3

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

131 Fixed Income Security Analysis 3 0 3

132 Actuarial Science-I 3 0 3

133 Financial Risk Management and Measurement 3 2 4

134 Principles of Financial Engineering 3 0 3

135 Stochastic Process in Finance 4 0 4

TOTAL 16 02 17

Second Year

TERM-4

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

241 Numerical Solution of Differential

Equation

3 2 4

242 Computational Modeling of Financial

Derivatives

3 2 4

243 Elective-I 3 0 3

244 Elective-II 3 0 3

245 Elective-III 3 0 3

TOTAL 15 4 17

TERM-5

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

251 Credit Derivative Pricing Models 2 2 3

252 Monte Carlo Methods in Financial

Engineering

3 2 4

6

253 Elective-IV 3 0 3

254 Elective-V 3 0 3

255 Dissertation (Preparatory Part) 0 0 4

TOTAL 11 4 17

TERM-6

Course

No.

Course Title No. of

lectures/week

Laboratory

work/week

Total

In hours In hours Credit

261 Dissertation and Viva 0 0 12

TOTAL 0 0 12

Courses for Electives I (243), II (244), IV (253) shall be chosen from the following

(GROUP-A)

A1. Actuarial Science II

A2. Quantitative Risk Management

A3. Advanced Topics in Financial Derivatives

A4. Dynamic Asset Management

A5. Optimization in Finance

A6. Time Series Analysis and Forecasting

Courses for Electives III (245),V (254) shall be chosen from the following

(GROUP-B)

B1. Soft Computing Methods in Finance

B2. Machine Learning with Financial Application

B3. Object Oriented Software Engineering

B4. Data Mining Techniques

B5.Parallal Computing

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TERM-1

111 STATISTICS AND PROBABILITY-I 3- 0- 3

1. Statistical data, Primary and secondary data, Attributes and variables: Discrete

and continuous. Diagrammatic representation: line diagram, pie and bar diagrams,

Pictograms and cartograms, graphs and tables.

2. Frequency distribution, Frequency polygon and Cumulative frequency polygon,

Histogram. Measures of central tendency mean, median, mode, quintiles.

Measures of dispersion, simple ideas about correlation and regression, Coefficient

of variation.

3. Deterministic and stochastic phenomena, classical definition of probability

computation of probability in simple situations, using permutation Combination

techniques. Axiomatic definition of probability. Equivalence of set & events,

union, intersection and complementation. Addition theorems. Conditional

probability, multiplication theorem, independence of events. Bayes Formula and

its applications.

4. Concept of a sample and a population, Frequency curve Probability distributions,

Binomial, Poisson and normal distributions their properties and fitting of

binomial, prison normal distribution. Probability mass function and probability

density functions.

5. Bivaniate distribution, conditional distribution and density function.

Independence of two random variables and Joint distribution, Transformation of

variables , Marginal and conditional distributions Mathematical expectation,

variance and moment Generating function. Probability Generating Function.

Books Recommended:

1. Introduction to Probability Theory and its Applications, Vol I, W. Feller (1972)

John Wiley.

2. Elementary Probability Theory K.L.Chung

3. An outline of Statistical Theory A.M.Goon, M.K.Gupta, B.Das Gupta VOL I-

Wiley eastern.

112 Mathematical Foundation 4 - 0 - 4

1. Sequences, limits, infinite series, tests of convergence, power series of functions,

Taylor's Theorem with remainder, convergence of power series, differentiation

and integration of power series.

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2. Functions of two or more variables, limits, continuity, partial derivatives, chain

rule, directional derivatives, gradient and tangent planes, higher order derivatives,

maxima and minima, Lagrange multipliers, Multiple integrals and change of co-

ordinates.

3. System of equations, vector matrix notations, vector spaces, bases and

dimensions, linear transformations, matrices, determinants, theory of linear

transformations, invariant subspaces, triangular form theorem, jordan canonical

forms.

4. Numerical Methods: Polynomial interpolation,(Lagrange’s and Newton’s

methods), Numerical integration (Newton cote’s formula, Gaussian method),

solution of nonlinear equations) Bisection method, Newton’s Method)

Books Recommended:

1. Calculus and Analytic Geometry, G.B. Thomas, R.L. Finney

2. Advanced Engineering Mathematics, E. Kreiszig

3. Advanced Engineering Mathematics (Alan Jeffrey)

4. Linear algebra, Hoffman and Kunze

5. Applied Numerical Analysis: C.F. Gerald & P.O. wheatley.

6. Burdan and Faires: Numerical Analysis.

113 Microeconomic Theory 3 -0 -3

1. Demand and supply, elasticity of demand and supply, market price determination,

price control-taxes and subsidies –case of open economy.

2. Theory of consumer behavior, consumer surplus, the theory of choice-utility

theory under uncertainty(axioms of choice under uncertainty, developing utility

functions, risk aversion ), state preference theory (uncertainty and alternative

future states, pure securities, No-arbitrage profit condition, economic

determination of security prices)

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3. Theory of production (production function with one or two variable inputs,

estimator of production function), cost theory ()cost concepts, short and long run

cost function), economic profits versus accounting profits, sunk costs, constrained

output maximization and cost minimization, profit maximization.

4. Perfect competition, Derivation of short run and long run supply curves,

monopoly, pricing strategies under monopoly, durable goods monopoly,

Auctions, Revenue-maximizing monopolist. Theory of oligopoly-Kinked demand

curve, Bertrand, cournot as stackelberg models, Nash equilibrium and subgame-

perfect equilibrium. Budent differentiation.

Books Recommended:

1. A. Sert- Microeconomics Theory and Applications, Oxford University Press

2. R.S. Pindyck and D.L. Rubinfeld, P.L.Meheta, Microeconomics, Pearson

Education.

3. Micro economic Theory-A Mathematical Approach J.M. Herderson and R.E.

Quardt, TMH

4. T.E. Copland, J.F. Weston, K. Sastri-Financial Theory and corporate policy-

Pearson.

114 Financial Instruments, Markets and Institutions 3- 0 -3

1. Financial Instruments: Non-market financial assets (Bank deposits, post office

deposits, company deposits, RPF), Money market instruments (Treasury bills,

certificates of deposits, Repos), Bonds, Common and preferred stock, Mutual

funds, indices, financial derivatives).

2. Financial Markets: Money and Capital Markets constituents, functions,

Deposit systems, Government securities markets, issuing and trading

securities, Role of SEBI-an overview, Recent developments.

3. Financial Institutions: Function and Management of Reserve Bank of India,

Commercial banks, Development Banks, Unit Trust of India, Non-Banking

Financial Institutions: Merchant banking, SEBI guidelines.

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Books Recommended:

1. L.M. Bhole- Financial Markets and Institutions.TMH

2. P.Chan..-Investment Analysis and Portfolio Management, TMH

3. M.Y.Khan-Indian Financial System, TMH

4. Fabozzi-Foundations of Financial Markets and Institutions, Pearson Education

5. Z. Bodie, A.Kare, A.J Marans, P.Mohanty-Investments-TMH.

115 Accounting for Decision Making 3 - 0 - 3

1. Conceptual Framework for Financial Accounting and Managerial Accounting,

Asset Equity Relations - Accounting Records.

2. Measurement of business income, Assets Accounting Depreciations, Sources of

Funds

3. Financial Statements, Legal Framework of Company Accounts, Financial

Statement Analysis.

4. Management Accounting, Cost Classification and Analysis, Statement of Cost,

Job and Process Costing.

5. Cost- Volume-Profit Analysis, Budgetary Control System Responsibility

Accounting.

Books Recommended

1. Financial Accounting –A Managerial Prospective-R. Narayanaswamy,

P.H.I.

2. Accounting Text and Cases –R.N.Anthomy, D.F. Hawkins, K.A.Merchant,

Tata Mcgraw hill

116 Programming in C++ 2 - 4 - 4

1. Introduction to C++ programming, Control structures (if, if/else, while, do/while,

for, for/ continue, switch, break)

2. Functions and Arrays

3. Pointers and strings

4. Classes and data abstraction,

5. Operator overloading, C++ stream input/ output

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Books Recommended: C ++ how to program, Deitel & Deitel , Pearson Education

TERM- 2

121 STATISTICS AND PROBABILITY-II 3 -0 -3

1. Conditional Expectation, Conditional Distribution, Weak and strong law of large

numbers, Modes of Convergence of random variables, Central Limit theorm(Without

proof).

2. Preliminaries on Stochastic process dealing with Random walk, Markov chain,

Poisson Processes, Birth and death processes and Brownian Motion. Martingale and

its some important properties.

3. Martingale in uses on Binomial pricing model and it’s limiting properties.

4. Likelihood function, Preliminaries on Maximum likelihood Estimation and Least

square Estimation with suitable examples Regression Analysis.

Tests of significance based on small samples, Preliminaries on Tests of hypothesis.

Books Recommended:

1. Probability Theory and Mathematical Statistics- V.K Rohatgi [Wieley Eastern]

2. An Outline of Statistical Theory- A.M.Goon, M.K Gupta, B.Dasgupta-Vol II

[Wiley Eastern]

122 Corporate Finance 4 - 0- 4

1. Rational expectation and market efficiency, Basic valuation principles, valuation

of debt and equity.

2. Term structure, cost of capital, Mutual fund, portfolio evaluation.

3. Equity research, capital structure, Dividend policy.

4. Cash flow analysis, capital budgeting under certainty, and capital budgeting under

uncertainty.

5. Balance of payments, Determination of Exchange rates, International capital

budgeting and investments.

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Books Recommended:

1. Essentials of Investment, Zvi Bodie

2. Finance, Zvi Bodie and Robert C. Merton, Prentice Hall

3. Multinational Financial Management, Alan C. Shapiro, Wiley.

4. Corporate Finance, Ross Westerfield and Jaffe, Irwin / Mc GrawHill

123 Portfolio Theory and Investment Analysis 3-0-3

1. Risk and risk aversion, Measuring risk and return of a single asset and portfolio.

Mean-Variance Portfolio Theory: Diversification, Forming Portfolios with on

assets, efficient frontier. The Markowitz model, the two-fund theorem, Inclusion

of a risk free asset, the one-fund theorem.

2. The capital Asset Pricing Model: Market equilibrium, Capital Market line, Pricing

Model, Security Market Line, Investment implications use of CAPM for

performance evaluation, CAPM as a Pricing formula.

3. Single and Multifactor models, CAPM as a factor model, Arbitrage pricing theory

(APT), APT and CAPM, Estimation of Parameters of mean-variance portfolio

theory, CAPM and APT. Tilting away from equilibrium.

4. Market Efficiency and behavioral Finance, Empirical Evidence on Security

returns, Evaluation of Portfolio Performance, Equity evaluation models,

International diversification. The process of portfolio management, the theory of

active portfolio management.

Books Recommended:

1. D.G. Luenberger- Investment Science, Oxford University Press.

2. Z. Bodie- A Kare, A.J Marcus, P.Mohanty-Investments, 6th

Edition, TMH

3. E.J.Elton.M.J Gruber-Modern Portfolio Theory and Investment Analysis- John

Wiley, Student Edition

4. T.E. Copeland, J. Fred Weston, K. Shastri, Financial Theory and Corporate

Policy- Addison Wesley.

124 Financial Derivatives 3 - 0 - 3

13

1. Introduction, Mechanics of futures markets, Hedging strategies using futures.

2. Determination of forward and futures prices, Interest rate futures, swaps.

3. Mechanics of options markets, Properties of stock options, Trading Strategies

involving options.

4. Binomial model for pricing options, Hedging strategies using Greeks, Derivative

markets in developing countries.

5. Options on stock indices, currencies and futures, volatility smiles.

Books Recommended

Text: Options, Futures and other Derivatives: - J. C. Hull, Prentice Hall of India, 7th

Edition. [Chapter 1 through 18 excluding 4, 12, 13]

References:

1. An Introduction to Derivatives and Risk Management, D. M. Chance, Thomson -

SPD- 2004

2. Derivatives - valuation and risk management, D. A. Dubofsky, T. W. Miller

Oxford Univ. Press -2003.

3. Mathematics for Finance an introduction to Financial Engineering, M. Capinski

T. Zastanniak , Springer Verlog - 2003

125 Financial Modeling using Excel 0 - 4 - 2

1. Basic financial calculations (PV, VPV, IRR, tables, future values)

2. Calculating the cost of capital

3. Financial Statement Modeling

4. Using Financial statement models for valuation

5. The Financial Analysis of Leasing

6. Portfolio Models

7. Calculators the variances - covariance Matrix

8. Calculating efficient portfolios when there are no short sale restrictions

9. Estimating Betas and the security Market Line

10. Computing option prices using binomial and Black Scholes models

14

11. Calculating Parameters of lognormal distribution

12. Computing early exercise boundaries of an American option

Books Recommended:

1. S. Benninga - Financial Modeling - MIT Press, 2000

2. M. Jackson, M. Staunton - Advanced Modeling in finance using Excel and VBA.

John Wiley, 2001.

126 C++ Design Patterns for Financial Derivatives 0-4- 2

(Note: Examples to be studied should be from financial derivatives)

1. Introduction to object oriented programming. Encapsulation, Polymorphsion

2. Inheritance and virtual functions, virtual construction and the bridge pattern

designing a statistics gatherer class, designing a random number generator class

and using it Monte Carlo simulation code.

3. Templates, standard template library (STL), use of template pattern for pricing

Asian Options use and for designing solver classes to determine implied validity.

4. The factory pattern, templasizing the factory, exceptions

5. Classification of design patterns as creational, structural and behavioral patterns,

interfacing with EXCEL physical design

Books Recommended

M.S. Joshi: C++ Design patterns and Derivative pricing, Second Edition,

Cambridge University press, 2008

D.J. Duffy: financial Instrument pricing using C++ John Wiley & Sons, 2004

TERM-3

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131 Fixed Income Security Analysis 3 -0-3

1. Bond characteristics, Bond Pricing, Bond yields, Bond prices over time.

2. Term structure of interest rates under certainty, interest rate uncertainty and

forward rate, forward rate agreements, theories term structure, measures the term

structure.

3. Interest rate sensitivity, duration, conversity, passive and active bond

management.

4. Interest rate derivatives (Bond options, interest rate caps and floors, hedging

interest rate derivatives, convexity, timing, and quanto adjustments).

Interest rate derivative models-Modes of short rate, HJM and LMM

5. Mortgage- Backed securities, and their analysis.

Books Recommended

1. Z. Bodie, A.Kane, A.J.Marchs, P. Mohanty-Investments, 6th

Editions, TMH, 2006

2. J.C.Hull- Options, Futures, and other derivatives- 7th

Edition- Peason Edition-

2009

3. Y.D. Lyuu- financial Engineering and Computation. Cambridge University Press

-2002

132 Actuarial Science-I 3 -0-3

1. (a) Life Table: Basic definitions, Probabilities, Constructing the life table from the

values of qs life expectancy choice of life tables, standard notation and

terminology. A sample table.

b) Life annuities: Calculating annuity premiums. The interest and survivorship

discount function, guaranteed payments, deferred annuities with annual

premiums, some practical considerations.

2. a) Life Insurance: Calculating life insurance premiums. Types of life insurance,

combined benefits, insurance viewed as annuities, summary of formulas, a

general insurance- annuity identity.

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b) Insurance and annuity reserves: The general pattern of reserves, recursion,

detailed analysis of an insurance or annuity contract, bases for reserves, no

forfeiture values, policies involving a return of the reserve, premium difference

and paid-up formulas.

c) Fractional durations: Cash flows discounted with interest only, life annuities

paid monthly, immediate annuities, approximation and computation, fraction

period premium and reserves, reserves at fractional durations.

3. a) Continuous payments: The force of discount, the constant interest case,

continuous life annuities, he force of morality, insurance payable at the moment

of death, premium and reserves, the general insurance-annuity identity in the

continuous case different equations for reserves, some examples of exact

calculation.

b) Select morality: Introduction, select and ultimate tables, changes in formulas.

4. Multiple-life contracts: The joint-life status, joint life annuities and insurances.

Last survivor annuities and insurances, moment of death insurances. The general

two life annuity contact. The general two life annuity contact, contingent

insurances, standard notation and terminology, spreadsheet applications.

5. a) Multiple-decrement theory: The basic model, insurances, determining the

model from the forces of decrement. The analogy with joint life statuses. A

Machine analogy, associated single determent tables.

b) Expenses: Effect on reserves, realistic reserve and balance calculations.

Books Recommended:

1. Actuarial Models (The Mathematics of Insurance)

By-Vladimir I. Rotar, Pub: Chapman and Hall, CRC

2. Fundamentals of Actuarial Mathematics

By- S. Dravid Promislow, Pub: Wiely

133 Financial Risk Management and Measurement 3 - 2- 4

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1. Regulation of financial Institutions. Need of regulation, credit risk and the

Basle accord, regulatory frame work in India, UK & US

2. Market Risk: key issues, Value at Risk (VaR) , Risk grades, capital adequacy

and market risk, yield validity and return validity, VaR for exchange rate risk.

3. VaR: Mapping cash Flows-VaR for equity portfolio, coupon paying bonds,

FAR, FRN and Suraps, FX forwards and options, VaR and the single index

model. Statistical issues of VaR – parameter estimation, nonparametric

measures of portfolio val, validation of forecasts, Monte Carlo simulation,

VaR and stress testing

4. Credit Risk: Credit metrics approach, measuring joint credit migration, types

of exposure, incentives and RAROC, Hedging and credit derivatives,

regulation, credit rating changes, credit risk of a swap, credit risk models

(structural approach, reduced from approach and empirical approach.

Books Recommended

1. Cutliberatson and Nitzsoche- Financial Engineering, Derivatives and Risk

Management, John Wiley

2. J.C.Hull: Option, Future and other derivatives , Pearson Education

3. G. Chako, A. Sjoman, H. Motolashi, V. Dessaiv- Credit Derivatives and primer

on credit risk, modeling and instruments-Wtarton school publication

134 Principle of Financial Engineering 3-0-3

1. Cast flow engineering and forwards contracts, engineering simple interest

derivatives.

2. Introduction to swap engineering, market strategy in financial engineering.

3. Dynamic replication methods and synthetics, option engineering applications.

4. Tools for volatility engineering, volatility swaps and volatility trading, smile

effects in engineering.

5. Credit derivatives in financial engineering, engineering of equity instruments.

Books Recommended:

Text: S.N.Neftci- Principles of financial engineering, Elsevier (2005)

135 Stochastic Processes in Finance 4 - 0 -4

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1. Brownian Motion: Brownian Motion as the limit of scaled Random walk.

Quadratic variation of Brownian Motion and it’s Markov property. First passage

time distribution and Reflection principle of Brownian Motion. Geometric

Brownian Motion and it’s Quadratic variation and it’s importance in Financial

modeling.

2. Stochastic Calculus: Ito integral and its quadratic valuation. Ito formula. Black-

Scholes, Metron Equation, Stochastic differential equation driven by Brownian

Motion and it’s solution (Proof not required), Samuelson Model. O.U. Process,

Mean reverting process and square root process and their solution process.

3. Introduction to Jump Processes: Compound Poisson Process, Jump process and

their integrals. Stochastic Calculus for Jump process and Quadratic Valuation.

4. Risk Neutral asset price modeling driven by Brownian Motion.

5. Interest Models: CIR Model, HJM Model, Hull White Model and Vasicek Model,

Solution Process of these models describes by S.D. Equations, Calculation of

Expectation and Variance of the solution processes.

Books recommended

1. Stochastic Calculus for Finance I and II by S. E. Shreve, Springer Verlag

2. Stochastic Process by J.Medhi (Wiley Eastern)

3. A First Course on Stochastic Process by S.Karlin & J. Tayler (Academic Press)

TERM-4

241 Numerical Solution of Differential Equations 3 - 2 - 4

1. Basic information on ODE. One step methods, convergence of one step methods,

Multi step methods (only examples).

2. Introducing Laplace, heat and wave equations, construction of finite difference

schems.

3. Solution of systems of linear equations. Gauss-Jordan algorithm, cholesky

decomposition, error bounds, elimination method for sparse matrices, singular

value decomposition, iteractive methods.

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4. Stability and convergence of finite difference methods, Crank Nicholson method,

ADI and splitting schemes for parabolic equations.

Books Recommended

1. Introduction to numerical analysis, J. Stoer and R. Bulirsch , Springer Verlag

2. Analysis of numerical methods, E. Issacson and H. B. Keller, John Wily, N.Y

3. Numerical Solution of PDE, G. D. Smith, Cambridge University, Pub.

4. Numerical Solution of PDE, K.W. Morton and D. F. Mayers.

5. Mathews- Numerical methods for science and engineering.

242 Computational Modeling of Financial Derivatives 3 - 2 - 4

1. The Black Scholes (B.S.) Model: Derivation of B.S. equation using no arbitrage

argument, options dividend paying equities, Derivation of B.S. formula for calls,

Puts and simple digitals, obtaining formulae for greeks and their numerical

computation, Finite Difference method for solution of B.S. equation.

2. Simple generalization of B.S. model (Dividend payments, time dependent

parameters), Early exercise and American options (Perpetual American call and

put, general payoff, local solutions), American option problem as free boundary

problems, Finite difference method for American options, Monte-Carlo

simulation.

3. Exotic and path dependent options : General introduction, Barrier options,

Strongly path dependent options, Asian options, Look back options, Multi Asset

options, Numerical implementation.

4. Extensions of B-S. Model: Defects in B-S Models, Discrete hedging, Transaction

costs, stochastic volatility. Jump diffusion, Crash modeling.

5. Numerical methods for pricing bonds and interest rate derivatives-finite

difference methods, Monte Carlo Simulation, Derivation of bond pricing PDE.

Books Recommended:

Text: Paul Wilmott: Paul Wilmott on quantitative finance John Wiley – 2006

AJG Carins- Interest rate models.

Reference:

1. Quantitative Methods in Derivative pricing - an introduction to computational

Finance, D. A. Tavella , John Wiley - 2002

20

2. The concepts and practice of mathematical finance, M. S. Joshi, Cambridge Univ.

Press - 2003.

3. Derivative Securities and Difference Methods, Y. Zhu, X. Wu, F. Chern, Springer

Verlag- 2004

TERM-5

251 Credit Derivative Pricing Models 2 - 2- 3

1. Credit Derivatives - Overview, hedge based Pricing, exotic credit derivatives,

Default correlation products and CDOs, credit linked notes.

2. Credit spreads and implied default probabilities, Recovery modeling, Building

blocks for credit derivatives pricing, pricing with the building blocks,

constructing, and calibrating credit spread curves implementation issues.

3. Advanced credit spread models - Poisson processes, Intromogeneous Poisson

Processes, stochastic credit spread, Recovery Modeling.

4. Implementation of Intensity - based models - Tractable models of the spot

intensity, computation of credit derivatives in the CIR model, Tree models, and

Partial differential equation based implementation, Term and structure of credit

spreads, Monte Carlo simulation.

5. Firm value and share price - based models pricing equations, solution to pricing

equations, Practical implementation, Unobservable firms values and credit grades,

advantages and disadvantages.

Books Recommended:

Texts:

1. P. J. Schonbucher - Credit derivatives Pricing Models- models, Pricing and

Implementation- John Wiley 2003.

2. G. Chacko, A.Sjoman, H. Motohasli, V.Dessain- Credit Derivatives-Wharton

School Publishing, 2007

References:

1. Paul Wilmott an Quantitative finance, P. Wilmott , John Wiley 2006

21

2. Quantitative Risk Management - Concepts, Techniques, Tools, A. J. Meiveils R.

Frey, P. Embrelts, Princton Univ. Press - 2005,

3. Credit Risk Pricing Models - theory and Practice, B. Schmid - Springer 2004.

252 Monte Carlo Methods in Finance Engineering 3-2-4

1. Principles of Monte Carlo, Generating random numbers and random variables:

Random number generation, general sampling methods, normal random variables.

2. Generating Sample paths: Brownian and Geometric Brownian motions; Gaussian

start rate methods; Square root diffusions; process with jumps; Forward rate

models; simple rates and continuous rates.

3. Variance Reduction Techniques.

4. Discretization methods.

5. Pricing American Options.

Books recommended:

Monte Carlo Methods in Financial Engineering, By Paul Glasserman,

Springer: Applications of Mathematics. 53, 2004.

ELECTIVES

A1. ACTUARIAL SCIENCE-II 3-0-3

1. Principles of premium calculation

Properties of premium principles, Examples of premium principles

2. The collective risk model

Reinsurance, The effect of reinsurance, Recursive calculation of aggregate claims

distributions, Extensions of the Panjer recursion formula, The application of

recursion formulae, Approximate calculation of aggregate claims distributions

3. The individual risk model

De Pril’s recursion formula, Kornya’s method, Compound Poisson

approximation, Numerical illustration

4. Introduction to ruin theory A discrete time risk model, The probability of ultimate ruin, The probability of

ruin in finite time, Lundberg’s inequality

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5. Classical ruin theory

The classical risk process, Poisson and compound Poisson process, Definitions of

ruin probability, The adjustment coefficient, Lundberg’s inequality, Survival

probability, Recursive calculation, Approximate calculation of ruin probabilities

Books Recommended:

1. Actuarial Models (The Mathematics of Insurance)

By - Vladimir I. Rotar

Chapman and Hall (CRC)

2. Fundamentals of Actuarial Mathematics

By – S. David Promislow

Wiley

3. Risk Analysis in Finance and Insurance

By – Alexandar Melnikov

Chapman and Hall (CRC)

4. International Series on Actuarial Science (Insurance Risk and Ruin)

David C.M.Dickson, Cambridge

A3. ADVANCED TOPICS IN FINANCIAL DERIVATIVES 3-0-3

1. Real Options: Martingales and measures (market price of risk, Martingales,

choices of numeroies, options to exchange one asset for another, change of

numeraire) capital investment appraisal, Extension of the risk-neutral valuation

frame work, estimating the market price of risk, Application to valuation of a

business, commodity price, Evaluating options in an investment opportunity.

2. Weather Derivatives: Weather derivatives, market weather contracts, modeling

temperature, parameter and volatility estimation, mean-reversion parameter

parameter estimation, pricing weather derivatives, Time-series weather

forecasting, pricing weather options in C++.

3. Energy and power derivatives: Electricity market, Electricity Pricing models,

swing options, Longstaff-schwartz algorithm for American and Bermundan

option. LSM algorithm pricing energy commodity derivatives, Jump diffusion,

Pricing models, Stochastic volatility pricing models, model parameter estimation,

Energy commodity models, Natural Gas Pricing models, Natural Gas and

Electricity swaps.

4. Power Markets, The PJ Model, Model calibration and its use for pricing options.

Option valuation methodology.

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5. Mental markets and mental pricing. Oil market creude and refined oil markets.

Books Recommended:

1. J.C.Hull- Option, Futures and other derivatives, Pearson Education.

2. J.London-Modeling Derivatives Applications in Matlab, C++, and Excel-

Financial Time Press, 2007

3. H.German-Commodities and commodity derivatives, John Wiley, 2005

A5. OPTIMIZATION IN FINANCE 3-0-3

1. Introduction to optimization problems. The Linear programming Problem,

Duality, Simplex methods, Sensitivity analysis of LP, Application to asset.

liability cash-flow matching, asset pricing and arbitrage.

2. Nonlinear Programming (NLP) Univariate optimization, Unconstrained and

constrained optimization, No smooth optimization, NLP Models.

3. Quadratic Programming (QP), optimality conditions, interior point methods, QP

models (mean-variance optimization, share ratio maximization, returns-based

style analysis).

4. Integer Programming (IP) theory and algorithms, IP models (constructing an

index fund, portfolio optimization with minimum transaction levels) Dynamic

Programming (DP) approach, DP model structuring asset-backed securities.

5. Stochastic Programming (SP) theory and algorithms, SP models (VaR,

conditional VaR, asset/liability management).

6. Decision making under competitive situations: Theory of Games.

Note: The midterm test shall consist of a written test and an assignment each of 15%

weightage.

Books Recommended:

Text: G. Cornuijols & R. Tutuneu-Optimization methods in finance-CUP-2007

Reference:

1. M.B.Biggs-Nonlinear Optimization with Finance Applications, Kluwer Academic

Publisher, 2005.

2. J. Nocedal & S.J. Wright-Numerical Optimization, Springer,2006

3. Hiller & Liberman-An introduction to Operations Research

A6. TIME SERIES ANALYSIS AND FORECASTING 3-0-3

1. Linear Time Series Analysis and its Applications

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Stationary, Correlation and Autocorrelation Function. White Noise and Linear

Time Series, Simple Autoregressive Models, Simple Autoregressive Models.

2. Conditional Hoteroscedastic Models.

Characteristic of Volatility, Structure of a Model, Model Building, The Arch

MODEL, The GARCH Model, The Integrated GARCH Model, The GARCH-M

Model, The Exponential GARCH Model, The threshold GARCH Model, The

CHARAM Model, Random Coefficient Autoregressive Models, The stochastic

Volatility Model, Application.

3. Nonlinear Models and Their Applications

Nonlinear Models, Nonlinearity Tests, Modeling, Forecasting, Applications.

4. High- Frequency Data Analysis and Market Microstructure

Nonsynchronous Trading, Bid-Ask Spread, Empirical Characteristics of

Transactions Data, Models for price changes, Duration Models, Nonlinear

Duration Models, Bivariate Models for Price Change and Duration.

5. Principle Component Analysis and Factor Models

A Factor Model, Macro econometric Factor Models, Fundamental Factor Models,

Principal Component Analysis, Statistical Factor Analysis, Asymptotic Principal

Component Analysis.

Books Recommended:

Analysis of Financial Time Series, by Ruey S. Tsay, Wiley Series in Probability

and Statistics

B1. SOFT COMPUTING METHODS IN FINANCE 3-0-3

Unit-1. Neural Network topologies, activation functions and learning methods,

perception training algorithm, The multilayer perception (MLP), Back Propagation

learning algorithm, financial applications.

Unit-2. Self organization maps, Support vector machine for classification and regression,

application to finance.

Unit-3. Genetic algorithm (GA), MLP-GA, SVM-GA hybrid methods and financial

applications.

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Unit-4. Elements of fuzzy set theory, Fuzzy logic and approximate reasoning, Neuro-

fuzzy and Fuzzy –GA hybrid methods, Rough set theory financial applications.

Unit-5. The particle swarm optimization algorithm, Discrete PSO, MLP-Swarm Hybrids,

Ant colony optimization methods, financial applications.

Books Recommended:

1. S.Haykin-Neural Networks: a comprehensive foundation, Pearson Education,

2001

2. Brabazan, M.O’ Neill-Biologically Inspired Algorithm for Financial Modelling-

Springer-2006

3. R.A. Aliev, B.Fazlollahi, R.R. Aliev-Soft Computing and its Applications in

Bussines and Economic, Springer Verlag, 2004.

4. Relevant research papers an use of soft computing methods for financial

problems.

B.2 Machine Learning with Financial Applications 3-0-3

1. Introduction to machine learning, Classification based on Bayes decision theory

(Losses and risks, Minimization of probability of classification error and average

risk. Discriminate functions and decision surfaces, Naïve Bayes classifier,

receiver operating curves), Probabilistic graphical models for machine learning

(Bayesian networks, Markov random fields), Expectation maximization

Algorithm, Financial applications. (T1, T2)

2. Supervised Learning using Neural Network-The Perceptron, Linearly separable

problems, Perceptron Convergence Theorem, Non-linearly separable problems,

Multi-Layer Perceptron and back propagation learning algorithm (BPA),

Heuristics for making BPA perform better, Modification of BPA using conjugate

gradient and Levenberg- Marquardt algorithms, Financial applications. (T3).

3. Supervised Learning Using Kernel Methods- Support Vector Machines (SVM)

for classification (Optimal hyperplanes for linearly and nonlinearly separable

patterns, Constructing SVM using inner product kernel, Algorithmic approaches

to solve quadratic programming, Multiclass SVMs, v-SVM) E- insensitive loss

functions, SVMs for nonlinear regression. Financial Applications (T3).

4. Unsupervised Learning- Dimensionality reduction (Curse of dimensionality,

Subset selection, Principal Component Analysis (PCA), Kernel PCA, Discrete

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time wavelet transform), Clustering (Basic concepts, K-means, Self-organizing

maps, Kernel clustering methods, Financial applications. (T1,T4).

Books Recommended:

T1. S.Theodoridis and K. Koutroumbas, Pattern Recognition, 4th

edition, Academic

Process, 2009.

T2. C.M.Bishop, Pattern Recognition and Machine Learning, Springer, 2006

T3. S. Haykin, Neural Networks-A Comprehensive Foundation, Pearson Education,

2001

T4. E. Alpaydin, Introduction to Machine Learning, MIT, 2004 (PHI-2006)

B3. OBJECT ORIENTED SOFTWARE ENGINEERING 3-0-3

Unit-1. Introduction, Software life cycle modules, Requirements Analysis and

specification, software design, Function oriented software design.

Unit-2. Coding and Testing, Software reliability and quality management, Computer

Aided Software Engineering, Software maintenance.

Unit-3. Introduction to object oriented Analysis and Design, Iterative Development and

the unified process, case study-The next-Gen POS, Inception, Understanding

Requirements, Use case Model, Indentifying other requirements.

Unit-4. Elaboration, Use case Model, Drawing system sequence diagrams, Visualizing

concepts, Adding Associations, Adding attributes, Adding details with operation

contracts, Interaction diagram notation.

Unit-5. PATTERNS, GRASP, Creating design class diagrams, GOF Design pattern

Planning and project queues comments on iterative development and the UP, Rational

Unified Process.

Text Book:

1. Crag Larman: Applying UML and Patterns-An introduction OOAP & D and the

Unified process, Pearson Education Asia.

2. Rajib Mail: Fundamentals of software Engineering, PHI.

B.4 DATA MINING TECHNIQUES 3-0-3

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1. Introduction: Fundamentals of Data Mining, Data mining Functionalities,

Classification of Data Mining systems, Major issues in Data Mining, OLAP

Technology for Data Mining, Multidimensional Data Model. Data Preprocessing:

Needs preprocessing the Data, Data Cleaning, Data Integration and

Transformation, Data Reduction, Discretization and Concept Hierarchy

Generation

Data Mining Primitives, Languages, and System Architectures: Data Mining

Primitives, Data Mining Query Languages.

2. Concepts Description: Characterization and Comparison: Data Generalization and

Summarization- Based Characterization, Analytical Characterization: Analysis of

Attribute Relevance, Mining Class Comparisons: Discriminating between

Different Classes.

Mining Association Rules in Large Databases: Association Rule Mining, Mining

Single Dimensional Boolean Association Rules from Transactional Databases.

3. Classification and Prediction: Issues Regarding Classification and Predication,

Classification by Decision Tree, Bayesian Network, Back propagation. Genetic

algorithms, Predication, Classifier accuracy, Financial Applications.

4. Cluster Analysis: Types of Data in Cluster Analysis, A Categorization of Major

Clustering Methods, Partitioning Methods, Density-Based Methods, Grid-Based

Methods, Model Based Clustering Methods outliner analysis. Mining Time series

and sequential data, Financial Applications.

Text Book:

Jiawei Han & Micheline Kamber Harcourt India. “Data Mining- Concepts and

Techniques”

Reference: Arun Kumar Pujari, Data Mining Techniques, University Press.

B.5 PARALLEL COMPUTING 3-0-3

1. Introduction to Parallel Computing –

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Motivation and scope. Parallel computing platforms, physical organization of

parallel computing platforms. Communication costs in parallel machines.

2. Principles of Parallel Algorithm Design-

(Decomposion, Tasks and interactions, mapping techniques for load balancing,

methods of containing interaction overheads, parallel algorithm model), Basic

communication operations.

3. Analytical modeling of parallel programs-

(Sources of overhead, performance metrics, scalability, asymptotic analysis of

parallel programs). Sorting on parallel computers (Sorting Networks, Quick sort)

4. Dense Matrix Algorithms-

Matrix-Vector multiplication, Matrix-Matrix multiplication, solving system of

linear equation-direct and interactive methods.

Text Book Recommended

A.Grma, A. Gupta, G. Karypis, V. Kumar. Introduction to Parallel Computing, Pearson

Education, Indian reprint, 2005

A. 2 Quantitative Risk Management 3-0-3 1. Basic concepts in risk management, Multivariate Models (Basic of multivariate

modeling, Normal mixture distributions, Dimension reduction techniques),

volatility models and risk estimation, fundamentals of multivariable time series,

multivariate GRACH Process.

2. Copulas and dependence ( Copulas, Dependence measures, Normal mixture

copulas, flitting copulas to data), Aggregate risk (coherent measures of risk,

bounds for aggregate risk capital allocation)

3. Extreme Value Theory (maxima, Tails of specific models, point process models,

multivariate maxima), operational risk and insurance analysis ( operational risk in

perspective, Elements of insurance analytics)

4. Credit risk management, (credit risk modeling threat hold, mixture monte carlo

models, Dynamic credit risk models (mathematical tools, financial and Actuarial

pricing of credit risk, pricing with doubly stochastic default time, conditionally

independent defaults)

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Book Recommended:

A.J.Mc Neil, R. Frey, and P. Embrechts- Quantitative Risk Management –Concept,

techniques, Tools. Princeton University Press, 2005

A. 4 Dynamic Asset Management 3-0-3 1. Dynamic Asset Pricing – Multiperiod mode, Dynamic Proffering approach, Infinite

horizon, setting, state prices and martingale measures, portfolio and consumption choice

equilibrium

2. Managing individual and institutional Investor portfolios, capital market expectations.

3. Asset allocation, fixed income portfolio management, equity portfolio management

Alternative Investments portfolio management

5. Execution of Portfolio Decisions, Monitoring and rebalancing, Evaluating

Portfolio performance, Global Investment performance standards

Books Recommended:

1. Darrell Deffie-Dynamic Asset Pricing Theory-Princeton University Press, 2001

2. J.L.Maginn, D.L. Tuttle, J.E. Pinto, D.W.Mcleavey,- Managing Investment

Portfolios-A Dynamic Process, CFA Institute, 2007