E22, QFFM_Prof_Ramana.pdf

7/28/2019 E22, QFFM_Prof_Ramana.pdf

1/5

Post Graduate Programme in Management2013-14 TERM: IV

TITLE OF THE COURSE: QUANTITIVE FOUNDATION OF FINANCIAL MARKETSCREDITS: 3

Name of the Faculty member Prof. L V Ramana

Faculty Block -C Room No.

Email: [email protected] Number 573

COURSE DESCRIPTION

The course seeks to familiarise participants with the tools that are required for understanding thedynamics of markets. This will be accomplished over three modules. The first module lays theeconomic foundations of markets, viz., the no-arbitrage criterion, and the mathematicalrepresentation of the same. The second module deals with statistical and other quantitativefoundations necessary to understand the randomness of markets. The third module seeks toimpart the main concepts in stochastic calculus.

COURSE OBJECTIVES

The objective of the course is to enhance participants understanding and application of thefollowing:

a) Arbitrage Theoremb) Probability Theoryc) Moments of Distributions and Markov processesd) Randomness in Financial Markets and the mathematical modelinge) Itos Lemma and Stochastic Differential Equations

PEDAGOGY/TEACHING METHOD:

In order to understand the concepts and techniques that form the quantitative underpinning offinancial markets, the focus would be on class lectures and discussion of approaches to solution ofproblems. Applications of concepts in the domain of arbitrage theorem, moments of distributions,Markov processes and an integrative view of stochastic calculus will be attempted throughempirical findings in specific markets.

TEXTAn Introduction to the Mathematics of Financial Derivatives, second edition, by Salih N Neftci(Academic Press 2000) denoted as SN


2/5

EVALUATION WeightageGroup Project 30%Quizzes 20%End-term examination 40%Class participation 10%Total 100%

Total 100%

SCHEDULE OF SESSIONSModule IEconomic Basis of Financial Markets and the Quantitative Framework in Finance

This module examines the economic underpinning of financial markets the absence ofarbitrage condition. It also deals with the development of quantitative models in finance.

Sessions 1 and 2 Role of Arbitrage Theorem in Financial Markets

Module ObjectiveObjective: The relevance of arbitrage theorem and the resulting risk neutral probabilities are thesubject matter of discussion. Implications of violation of no-arbitrage condition are examined withhigh frequency data of stocks traded simultaneously in two markets

Readings.

Sessions and ObjectiveCh. 2 (SN) Sections 1 to 5

An Apertif on Arbitrage, from Introduction to the Mathematics of Finance: From RiskManagement to Options Pricing, Steven Roman, Springer 2000

Comparing High Frequency Data of Stocks that are traded simultaneously in the US andGermany: Simulated versus Empirical Data Eurasian Economic Review, 1(2), 2011, pp126-142

Session 3 Role of Mathematical Models in Finance

Objective: This session discusses the contributions of mathematics to the development ofthe discipline of finance

Readings

Influence of Mathematical Models in Finance on Practice: Past, Present and Future,

Robert C Merton, Financial Practice and Education, Spring / Summer 1995, pp 7 -15

Mathematicians in the black, Weston, James, July 2007, 77, 6, pp 26-29


3/5

Module II Tools in Quantitative modeling

This module is geared towards providing the quantitative foundation of randomness

Sessions 4 and 5 Probability and Applications of Moments in Finance

Module ObjectiveObjective: These sessions are intended to refresh tools in probability theory such as randomvariable, distribution function and moments of a distribution. Understanding moments in specificfinancial models and the implications are also sought to be understood.

Sessions and Objective

Readings

Ch. 5 (SN) Sections 1 to 5

Comparing the Single Index Model with the Markowitz model (excerpt from a chapter)

Downside Risk Analysis applied to Hedge Funds Universe Josep Perello, Physica A 383,pp 480 496

Sessions 6 and 7 Markov Chains and Its Applications

Objective: Understanding asset movement between states incorporating probabilitytransition matrices is sought to be accomplished by examining the statistical concepts

relating to discrete Markov Chains. The use of transition probability matrices in theJapanese index futures and credit rating industry are sought to be understood.

Readings

Ch. 7 Markov Chains from the Schaums outline text (on Probability and Statistics)

A New Methodology for Studying Intraday Dynamics of Nikkei Index Futures usingMarkov Chains, Wang Shiyun, Lim Kian Guan, and Carolyn Chang, Journal ofInternational Financial Markets, Institutions and Money 9 (1999), pp 247-265

Dynamics of Rating Transition, Reza Bahar and Krishan Nagpal, Algo ResearchQuarterly, Vol 4, Nos. 1/2, March-June 2001

Module III Module III Stochastic Calculus

This module deals with randomness in asset markets that are amenable to stochasticmodeling

Module Objective


4/5

Sessions and ObjectiveSession 8 Differentiation in Stochastic Environment

The notion of differentiation in stochastic environments is sought to be distinguished fromdifferentiation in deterministic environment. The resulting implications for volatility and its boundsare explored.

Readings


Itos Calculus in Financial Decision Making, A G Malliaris, SIAM Review, Vol. 25, No. 4, October1983

Sessions 9 and 10 Wiener Process

Objective: The objective of these sessions is to explain the features of Wiener process that

characterize normal events. Variations in the underlying model that need to be made so as toincorporate rare events are also examined.

Readings


How Much trust should Risk Managers place on Brownian Motions of Financial Markets?,Shaheen Borna and Dheeraj Sharma, International Journal of Emerging Markets, Vol. 6, No. 1,2011, pp 7 16

Sessions 11 and 12 Itos Lemma

Objective: These sessions are centered around the heart of stochastic calculus, viz., ItosLemma. This model helps in understanding the change in movement of a random variable that isbased on the movement of another random variable and a deterministic variable such as timeelapsed. The application of Itos Lemma in the context of the Black-Scholes model is alsoexamined.

Readings

Ch. 10 (SN) Sections 1 to 4 (in session 11)Ch. 11 (SN) Sections 5 to 8 (in session 12)

Session 13 Stochastic Differential Equations (SDEs)

Objective: The different forms of SDEs and testing out candidate solutions that satisfy an SDE isthe subject matter of this session

Reading



5/5

Session 14 Partial Differential Equations (PDEs)

Objective: A simple heuristic model to derive the PDE used in Black-Scholes equation is sought tobe understood in the backdrop of a self-financing portfolio.

Reading


Session 15 Stochastic Calculus in Financial Markets

Objective: Integrating the techniques of stochastic calculus to an applied setting is sought to beaccomplished in this session

Reading

Visualizing the Stochastic Calculus of Option Pricing with Excel and VBA, Tom Arnold andStephen C Henry, Journal of Applied Finance, Spring / Summer 2003, pp 56 65.

* * * *

Documents

E22, QFFM_Prof_Ramana.pdf