NPTEL - Path Integral Methods in Physics & Finance
offered by IIT Roorkee

Public/Government Institute
Estd. 1847

Path Integral Methods in Physics & Finance
at
IIT Roorkee
Overview

Knowledge of the nuances of the 'path integral-formalism of QFT is indispensable for academic progression in this area

Duration	12 weeks
Mode of learning	Online
Credential	Certificate

Path Integral Methods in Physics & Finance
at
IIT Roorkee
Highlights

Earn a E- certificate of completion from IIT Roorkee

Path Integral Methods in Physics & Finance
at
IIT Roorkee
Course details

Skills you will learn

Bonds Financial modelling Risk Management Valuation

More about this course

The applications of this versatile concept are also growing by the day, one of the cardinal ones being in pricing of complex financial assets
Scientific risk management by the investor fraternity has become of cardinal necessity for generating competitive returns and surviving in the marketplace

Path Integral Methods in Physics & Finance
at
IIT Roorkee
Curriculum

Week 1

Motivation

Rationale & concept of path integrals

Elements of probability distributions

Moments & Cumulants & their generating functions

Binomial & Gaussian distributions

Laplace &Stirling formula

Week 2

Gaussian integrals of matrix functions

The Central Limit Theorem

Elementary theory of stochastic processes

Chapman Kolmogorov equation

Master equation

Kramer Moyal equation

Fokker Planck equation

Random Walks & Brownian motion

Week 3

Path integral solution of diffusion equation

Feynman Kac formula

Autocorrelators

Langevin equation

Path integral solution of Schrodinger equation &Langevin equation

Week 4

Fokker Planck vs Langevin equations

Determinism vs Classical & Quantum randomness

Basic theory of QM path integral

Introduction to the QM machinery & notational conventions

Equivalence of Schrodinger & Heisenberg pictures

Single particle non-relativistic QM path integral

Week 5

QM Harmonic Oscillator path integral

Equivalence between Schrodinger & path integral approaches

Correlation functions

Relevenace of functional derivatives

Week 6

Relativistic path integral

Saddle point approach to path integral

Interpretation of QM path integral

Causality violation

Need for QFT

Week 7

0-Dimensional Field Theory

Correlation Functions

Generating Functionals

Field interactions

Perturbative expansions

Convergence issues

Propagators

Feynman Rules

Schwinger-Dyson Equation

Week 8

SDE from Feynman Diagrams

Loop expansions

Limiting behavior

Saddle point approximation

Effective field

Renormalization

1-D field theory

Feynman Rules & SDE

Propagator

SDE in terms of propagators

Explicit expression for propagator

Generalization to D-dimensions

Continuum limits

Week 9

Mode space computations

Divergences

Loop integrals

Generatingfunctionals

Correlators and allied results in D- Dimensional Euclidean space

Field theory in Minkowski space

Scalar field generating functional

Week 10

Scalar field propagator & correlators

Fourier integrals

Causality

Interacting field in Minkowski space

Important identities

Derivation of SDE,Fermionic fields & their path integral quantization

Week 11

Maxwell equations & gauge field quantization

Their path integral

Fluctuation properties official assets

Brownian motion & Ito's lemma

Lognormal distribution & stock price distribution

Formulation of & solution to the Fokker Planck equation for stock price model

Week 12

Basic theory of options

Profit diagrams

Put-Call parity

Option pricing

The Binomial &Black Scholes Models

Risk Neutral valuation

American options

Derivation of and solution to the Black-Scholes PDE

Path integral approach to pricing of path independent options

Path integral valauation of other cash flow structures e.g. zero coupon bonds etc

Path Integral Methods in Physics & Finance
at
IIT Roorkee
Faculty details

Prof. J. P. Singh

Jatinder Pal Singh, is a Professor at the Indian Institute of Technology Roorkee. He is also a postgraduate in Physics, Mathematics and a graduate in Law & Operational Research.