Change of measure and Girsanov's Theorem

Derives Black Scholes formula for a European Call option

Explains Martingale Representation Theorem and creation of hedge portfolio

Explains multi dimensional Girsanov and Martingale Representation Theorem

Describes First Fundamental Theorem of Asset Pricing

Describes Second Fundamental Theorem of Asset Pricing

Derives closed form solution for European Call on dividend paying stock

Derives closed form solution for European Call on dividend paying stock

Futures & Forward contract on non-dividend paying assets

Stochastic Differential Equations and Markov Property

Describes Feyman-Kac Theorem

Applies Feynmac-Kac to Interest Rate Models

Multi-dimensional Feynman-Kac and application to Asian Options

describes the reflection principle

Computes Joint Density of Brownian Motion with Drift and its Maximum

Computes closed form solution for up & out call option

Derives differential equation for up and out call

Derives PDE for a lookback option

Derives formula for Lookback Option

Derives PDE for asian options

Derives PDE for asian options using change of numeraire

Computes the price of a perpetual American put option

American Call on Non-Dividend Paying Stock

American Call on Dividend Paying Stock