Program

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Module Three

Equity, Currency and Commodity Derivatives

The Black-Scholes theory, built on the principles of delta-hedging and no arbitrage, has been very successful and fruitful as a theoretical model and in practice. The theory and results are explained using different kinds of mathematics to make the student familiar with techniques in current use.

 

Estimating Volatility using Time Series Data

•    Different types of volatility
•    Simple Moving Average
•    Autoregressive Conditional Heteroscedasticity (GARCH)
•    Exponential Weighted Moving Average
•    Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
•    Parameter Estimation using Maximum Likelihood

 

Black-Scholes Model

•    The assumptions that go into the Black-Scholes equation
•    Foundations of options theory: delta hedging and no arbitrage
•    The Black-Scholes partial differential equation
•    Modifying the equation for commodity and currency options
•    The Black-Scholes formulae for calls, puts and simple digitals
•    The meaning and importance of the Greeks, delta, gamma, theta, vega and rho
•    American options and early exercise
•    Relationship between option values and expectations

 

Understanding Volatility

•    The many types of volatility
•    What the market prices of options tells us about volatility
•    The term structure of volatility
•    Volatility skews and smiles
•    Volatility arbitrage: Should you hedge using implied or actual volatility?

 

Trading Simulator – Trading Equity Options

•    Introducing equity options
•    Speculate and hedge by managing Greeks exposure
•    Employing common options trading strategies

 

Martingale Theory-Application to Option Pricing

•    The Greeks in detail
•    Delta, gamma, theta, vega and rho
•    Higher-order Greeks
•    How traders use the Greeks

 

Martingales and PDE's: Which, When and Why Part I

•    Computing the price of a derivative as an expectation
•    Girsanov's theorem and change of measures
•    The fundamental asset pricing formula
•    The Black-Scholes Formula
•    The Feynman-K_ac formula
•    Extensions to Black-Scholes: dividends and time-dependent parameters
•    Black's formula for options on futures

 

Monte Carlo and Finite Differences

•    The justification for pricing by Monte Carlo simulation
•    Grids and discretization of derivatives
•    The explicit finite-difference method
 

Advanced Greeks

•    The names and contract details for basic types of exotic options
•    How to classify exotic options according to important features
•    How to compare and contrast different contracts
•    Pricing exotics using Monte Carlo simulation
•    Pricing exotics via partial differential equations and then finite difference methods