Overview

Explore advanced mathematical models for pricing financial instruments in this comprehensive 17-hour course from the California Institute of Technology. Delve into stocks, bonds, forwards, swaps, and options, learning to apply risk-neutral pricing, binomial tree models, and the Black-Scholes-Merton framework. Master stochastic calculus concepts, including Brownian motion and Itô's lemma, to price exotic options and handle stochastic volatility. Investigate interest rate and credit risk models, and develop hedging strategies using futures, bonds, and portfolio sensitivities. Gain a deep understanding of financial mathematics to excel in quantitative finance and risk management.

Syllabus

1 1 Welcome to my course - BEM1105x Course - Prof. Jakša Cvitanić.
1 2 Overview.
1 3 Stocks, bonds, forwards Part I.
1 4 Stocks, bonds, forwards Part II.
1 5 Swaps.
1 6 Call and Put Options Part I.
1 7 Call and Put Options Part II.
1 8 Call and Put Options Part III.
1 9 Options combinations Part I.
1 10 Options combinations Part II.
2 1 Pricing deterministic payoffs Part 1.
2 2 Pricing deterministic payoffs Part 2.
2 3 Bonds Part 1.
2 4 Bonds Part 2.
2 5 Bonds Part 3.
3 1 Model independent relations forwards, futures and swaps Part 1.
3 2 Model independent relations forwards, futures and swaps Part 2.
3 3 Model independent relations forwards, futures and swaps Part 3.
3 4 Model independent relations forwards, futures and swaps Part IV.
3 5 Model independent relations options Part 1.
3 6 Model independent relations options Part 2.
3 7 Model independent relations options Part 3.
4 1 Discrete time models.
4 2 Risk neutral pricing Part 1.
4 3 Risk neutral pricing Part 2.
4 4 Risk neutral pricing Part 3.
4 5 Fundamental theorems of asset pricing Part 1.
4 6 Fundamental theorems of asset pricing Part 2.
4 7 Binomial tree pricing Part 1.
4 8 Binomial tree pricing Part 2.
5 1 Brownian motion process Part 1.
5 2 Brownian motion process Part 2.
5 3 Stochastic integral Part 1.
5 4 Stochastic integral Part 2.
5 5 Ito s Rule, Ito s Lemma Part 1.
5 6 Ito s Rule, Ito s Lemma Part 2.
6 1 Black Scholes Merton pricing Part 1.
6 2 Black Scholes Merton pricing Part 2.
6 3 Black Scholes Merton pricing Part 3.
6 4 Risk neutral pricing Black Scholes Merton model Part 1.
6 5 Risk neutral pricing Black Scholes Merton model Part 2.
6 6 Black Scholes Merton pricing Part 3.
7 1 Variations on Black Scholes Merton Part 1.
7 2 Variations on Black Scholes Merton Part 2.
7 3 Currency options Part 1.
7 4 Currency options Part 2.
7 5 Exotic options Part 1.
7 6 Exotic options Part 2.
7 7 Pricing options on more underlyings Part 1.
7 8 Pricing options on more underlyings Part 2.
8 1 Stochastic Volatility Part 1.
8 2 Stochastic Volatility Part 2.
8 3 Stochastic Volatility Part 3.
8 4 Jump diffusion models.
9 1 Static hedging with futures Part 1.
9 2 Static hedging with futures Part 2.
9 3 Static hedging with bonds.
9 4 Perfect hedging replication Part 1.
9 5 Perfect hedging replication Part 2.
9 6 Hedging portfolio sensitivities Part 1.
9 7 Hedging portfolio sensitivities Part 2.
9 8 Hedging portfolio sensitivities Part 3.
10 1 Introduction to interest rate models Part 1.
10 2 Introduction to interest rate models Part 2.
10 3 Continuous time interest rate models Part 1.
10 4 Continuous time interest rate models Part 2.
10 5 Continuous time interest rate models Part 3.
10 6 Continuous time interest rate models Part 4.
10 7 Forward rates models Part 1.
10 8 Forward rates models Part 2.
10 9 Forward rates models Part 3.
10 10 Forward rates models Part 4.
10 11 Change of numeraire method Part 1.
10 12 Change of numeraire method Part 2.
10 13 Introduction to credit risk models Part 1.
10 14 Introduction to credit risk models Part 2.