Computational Finance Lecture Series

Notes from the Computational Finance YouTube lecture series.

Contents

Lecture 1: Introduction and Overview of Asset Classes

• Market share of different asset classes
• Equities and stochastic behaviour of stocks
• The money market and interest rates
• Time value of money

Lecture 2: Stock, Options and Stochastics

• Trading of options and hedging
• Commodities, currencies and cryptocurrencies
• Value of call/put options
• Wiener process and stochastic processes
• Geometric Brownian Motion (GBM)
• Ito's Lemma for solving SDEs

Lecture 3: Option Pricing and Simulation in Python

• Black-Scholes model
• Hedging with Black-Scholes
• Martingales and option pricing
• Risk neutral valuation and Feynman-Kac formula
• Measures and impact on drift
• Closed-form solution for Black-Scholes

Lecture 4: Implied Volatility

• Key elements when pricing derivatives
• Black-Scholes implied volatility
• Newton-Raphson method for finding IV
• Time-dependent volatility parameter
• Implied volatility surface (smile, skew, hockey stick)
• Deficiencies of the Black-Scholes model

Lecture 5: Jump Processes

• Inclusion of jumps in stock processes
• Poisson process
• Ito's Lemma with jumps
• Asset dynamics under Q-measure with jumps
• Partial Integro-Differential Equations (PIDE)
• Merton's model and Kou's model
• Characteristic function for jump processes

Lecture 6: Affine Jump Diffusion Processes

• Choosing a pricing method
• Fourier transformation motivation
• Characteristic function for Black-Scholes
• Affine diffusion processes
• Duffie-Pan-Singleton approach
• Characteristic function for high dimensions

Lecture 7: Stochastic Volatility Models

• Deficiencies of Black-Scholes
• The Heston stochastic volatility model
• CIR (Cox-Ingersoll-Ross) process for variance
• Noncentral chi-squared distribution
• Feller condition

Additional Notes

• Course Terminology and Common Themes
• Overview