Pricing Options with Mathematical Models
This is an introductory course on options and other financial derivatives, and their applications to risk management. We will start with defining derivatives and options, continue with discrete-time, binomial tree models, and then develop continuous-time, Brownian Motion models. A basic introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also discuss more general models, such as stochastic volatility models.
Buy Now AED 170.99 + VAT
Monthly Subscription Starting at AED 99 + VAT
- Level Professional
- Duration 69 hours
- Course by Caltech
-
Offered by
About
This is an introductory course on options and other financial derivatives, and their applications to risk management. We will start with defining derivatives and options, continue with discrete-time, binomial tree models, and then develop continuous-time, Brownian Motion models. A basic introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also discuss more general models, such as stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the probabilistic, martingale approach. We will also cover an introduction to modeling of interest rates and fixed income derivatives. I teach the same class at Caltech, as an advanced undergraduate class. This means that the class may be challenging, and demand serious effort. On the other hand, successful completion of the class will provide you with a full understanding of the standard option pricing models, and will enable you to study the subject further on your own, or otherwise. Prerequisites. A basic knowledge of calculus based probability/statistics. Some exposure to stochastic processes and partial differential equations is helpful, but not mandatory. It is strongly recommended you take the prerequisites test available in Unit 0, to see if your mathematical background is strong enough for successfully completing the course. If you get less than 70% on the test, it may be more useful to work further on your math skills before taking this course. Or you can just do a part of the course.Modules
Welcome and Pre-Course Information
-
1
Readings
1
Readings
- Welcome
Pre-requisites Assessment
-
1
Readings
-
1
Assignment
1
Assignment
- Pre-requisite self assessment
1
Readings
- Intro to problems in the Pre-requisites Assessment
Welcome and Overview
-
2
Videos
2
Videos
- Welcome to my course - Video
- Video - Overview
Stocks, bonds, forwards
-
2
Videos
2
Videos
- Stocks, bonds, forwards - Part 1 Video
- Stocks, bonds, forwards - Part 2 Video
Swaps
-
1
Videos
1
Videos
- Video - Swaps
Call and put options
-
3
Videos
3
Videos
- Call and put options - Part 1 Video
- Call and put options - Part 2 Video
- Call and put options - Part 3 Video
Options combinations
-
2
Videos
2
Videos
- Options combinations - Part 1 Video
- Options combinations - Part 2 Video
Unit 1 Practice Problems and Problem Set 1
-
2
Assignment
2
Assignment
- Unit 1 Practice Problems
- Problem Set 1
Slides for Unit 1
-
1
Readings
1
Readings
- Unit 1 slides
Pricing deterministic payoffs
-
2
Videos
2
Videos
- Pricing deterministic payoffs - Part 1 Video
- Pricing deterministic payoffs - Part 2 Video
Bonds
-
3
Videos
3
Videos
- Bonds - Part 1 Video
- Bonds - Part 2 Video
- Bonds - Part 3 Video
Unit 2 Practice Problems and Problem Set 2
-
2
Assignment
2
Assignment
- Unit 2 Practice Problems
- Problem Set 2
Slides for Unit 2
-
1
Readings
1
Readings
- Unit 2 slides
Model independent relations - forwards, futures and swaps
-
4
Videos
4
Videos
- Model independent relations - forwards, futures and swaps - Part 1 - Video
- Model independent relations - forwards, futures and swaps - Part 2 - Video
- Model independent relations - forwards, futures and swaps - Part 3 - Video
- Model independent relations - forwards, futures and swaps - Part 4 - Video
Model independent relations - options
-
3
Videos
3
Videos
- Model independent relations - options - Part 1 - Video
- Model independent relations - options - Part 2 - Video
- Model independent relations - options - Part 3 - Video
Problem set 3 and practice problems
-
2
Assignment
2
Assignment
- Unit 3: Practice Problems
- Problem Set 3
Slides for Unit 3
-
1
Readings
1
Readings
- Slides for Unit 3
Discrete-time models
-
1
Videos
1
Videos
- Discrete-time models - Video
Risk-neutral pricing
-
3
Videos
3
Videos
- Risk-neutral pricing - Part 1 - Video
- Risk-neutral pricing - Part 2 - Video
- Risk-neutral pricing - Part 3 - Video
Fundamental theorems of asset pricing
-
2
Videos
2
Videos
- Fundamental theorems of asset pricing - Part 1 - Video
- Fundamental theorems of asset pricing - Part 2 - Video
Binomial tree pricing
-
2
Videos
2
Videos
- Binomial tree pricing - Part 1 - Video
- Binomial tree pricing - Part 2 - Video
Problem set 4 and practice problems
-
2
Assignment
2
Assignment
- Unit 4 Practice Problems
- Problem Set 4
Slides for Unit 4
-
1
Readings
1
Readings
- Slides for Unit 4
Brownian motion process
-
2
Videos
2
Videos
- Brownian motion process - Part 1 - Video
- Brownian motion process - Part 2 - Video
Stochastic integral
-
2
Videos
2
Videos
- Stochastic integral - Part 1 - Video
- Stochastic integral - Part 2 - Video
Ito's rule
-
2
Videos
2
Videos
- Ito's Rule, Ito's Lemma - Part 1 - Video
- Ito's Rule, Ito's Lemma - Part 2 - Video
Problem set 5 and practice problems
-
2
Assignment
2
Assignment
- Unit 5 Practice Problems
- Problem Set 5
Slides for Unit 5
-
1
Readings
1
Readings
- Slides for Unit 5
Black-Scholes-Merton pricing
-
3
Videos
3
Videos
- Black-Scholes-Merton pricing - Part 1 - Video
- Black-Scholes-Merton pricing - Part 2 - Video
- Black-Scholes-Merton pricing - Part 3 - Video
Risk-neutral pricing - Black-Scholes-Merton model
-
3
Videos
3
Videos
- Risk-neutral pricing - Black-Scholes-Merton model - Part 1 - Video
- Risk-neutral pricing - Black-Scholes-Merton model - Part 2 - Video
- Risk-neutral pricing - Black-Scholes-Merton model - Part 3 - Video
Problem set 6 and practice problems
-
2
Assignment
2
Assignment
- Unit 6 Practice Problems
- Problem Set 6
Slides for Unit 6
-
1
Readings
1
Readings
- Slides for Unit 6
Variations on Black-Scholes-Merton
-
2
Videos
2
Videos
- Variations on Black-Scholes-Merton - Part 1 - Video
- Variations on Black-Scholes-Merton - Part 2 - Video
Currency options
-
2
Videos
2
Videos
- Currency options - Part 1 - Video
- Currency options - Part 2 - Video
Exotic options
-
2
Videos
2
Videos
- Exotic options - Part 1 - Video
- Exotic options - Part 2 - Video
Pricing options on more underlyings
-
2
Videos
2
Videos
- Pricing options on more underlyings - Part 1 - Video
- Pricing options on more underlyings - Part 2 - Video
Problem set 7 and practice problems
-
3
Assignment
3
Assignment
- Unit 7 Practice Problems
- Problem Set 7
- Bonus Problem
Slides for Unit 7
-
1
Readings
1
Readings
- Slides for Unit 7
Static hedging with futures
-
2
Videos
2
Videos
- Static hedging with futures - Part 1 - Video
- Static hedging with futures - Part 2 - Video
Static hedging with bonds
-
1
Videos
1
Videos
- Static hedging with bonds - Video
Perfect hedging - replication
-
2
Videos
2
Videos
- Perfect hedging - replication - Part 1 - Video
- Perfect hedging - replication - Part 2 - Video
Hedging portfolio sensitivities
-
3
Videos
3
Videos
- Hedging portfolio sensitivities - Part 1 - Video
- Hedging portfolio sensitivities - Part 2 - Video
- Hedging portfolio sensitivities - Part 3- Video
Problem set 8 and practice problems
-
2
Assignment
2
Assignment
- Unit 8 Practice Problems
- Problem Set 8
Slides for Unit 8
-
1
Readings
1
Readings
- Slides for Unit 8
Stochastic Volatility
-
3
Videos
3
Videos
- Stochastic Volatility - Part 1 - Video
- Stochastic Volatility - Part 2 - Video
- Stochastic Volatility - Part 3 - Video
Jump-diffusion models
-
1
Videos
1
Videos
- Jump-diffusion models - Video
Slides for Unit 9
-
1
Readings
1
Readings
- Slides for Unit 9
Introduction to interest rate models
-
2
Videos
2
Videos
- Introduction to interest rate models - Part 1 - Video
- Introduction to interest rate models - Part 2 - Video
Continuous-time interest rate models
-
4
Videos
4
Videos
- Continuous-time interest rate models - Part 1 - Video
- Continuous-time interest rate models - Part 2 - Video
- Continuous-time interest rate models - Part 3 - Video
- Continuous-time interest rate models - Part 4 - Video
Forward rates models
-
4
Videos
4
Videos
- Forward rates models - Part 1 - Video
- Forward rates models - Part 2 - Video
- Forward rates models - Part 3 - Video
- Forward rates models - Part 4 - Video
Change of numeraire method
-
2
Videos
2
Videos
- Change of numeraire method - Part 1 - Video
- Change of numeraire method - Part 2 - Video
Introduction to credit risk models
-
2
Videos
2
Videos
- Introduction to credit risk models - Part 1 - Video
- Introduction to credit risk models - Part 2 - Video
Unit 10 Quizzes
-
2
Assignment
2
Assignment
- Unit 10 Practice Problems (for Problem Set 9)
- Problem Set 9 (in Unit 10)
Slides for Unit 10
-
1
Readings
1
Readings
- Slides for Unit 10
Final Exam (number of attempts is limited)
-
1
Readings
-
2
Assignment
2
Assignment
- Final Exam, Part 1: Multiple Choice
- Final Exam, Part 2: Calculations
1
Readings
- Introduction to the Final Exam
Auto Summary
"Pricing Options with Mathematical Models" is an advanced course offered by Coursera, focusing on financial derivatives and risk management. Taught by a Caltech instructor, it covers binomial tree models, Brownian Motion, Black-Scholes-Merton pricing, stochastic volatility models, and interest rate modeling. Intended for learners with a calculus-based probability background, the course demands serious effort but promises a comprehensive understanding of option pricing models. It spans 4140 minutes and offers Starter, Professional, and Paid subscription options. Ideal for professionals seeking deep insights into financial mathematics.
Jaksa Cvitanic