California Institute of Technology Courses

Nature's Constituents

5

With the discovery of the Higgs particle in 2013, the Standard Model came closer to being a complete theory. In this Master Class, Maria Spiropulu, Professor of Physics at Caltech, examines the robustness of the Standard Model, and takes a look at the future of particle physics.

Learning From Data (Introductory Machine Learning)

4.5

This introductory computer science course in machine learning will cover basic theory, algorithms, and applications. Machine learning is a key technology in Big Data, and in many financial, medical, commercial, and scientific applications. It enables computational systems to automatically learn how to perform a desired task based on information extracted from the data. Machine learning has become one of the hottest fields of study today and the demand for jobs is only expected to increase. Gaining skills in this field will get you one step closer to becoming a data scientist or quantitative analyst.This course balances theory and practice, and covers the mathematical as well as the heuristic aspects. The lectures follow each other in a story-like fashion:What is learning?Can a machine learn?How to do it?How to do it well?Take-home lessons.

Pricing Options with Mathematical Models

0

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 1Discrete 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 Part2.6 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.

Accelerate, Collide, Detect

0

Explore particle accelerators, one of the most effective tools for understanding particle physics, with Nobel Laureate Barry Barish, who led the design of the International Linear Collider. Delve into the future of this groundbreaking technology that is pushing the limits of physics. 

Learning from Data (Introductory Machine Learning course)

4.6

This is an introductory course in machine learning (ML) that covers the basic theory, algorithms, and applications. ML is a key technology in Big Data, and in many financial, medical, commercial, and scientific applications. It enables computational systems to adaptively improve their performance with experience accumulated from the observed data. ML has become one of the hottest fields of study today, taken up by undergraduate and graduate students from 15 different majors at Caltech. This course balances theory and practice, and covers the mathematical as well as the heuristic aspects. The lectures below follow each other in a story-like fashion:What is learning?Can a machine learn?How to do it?How to do it well?Take-home lessons.

Pricing Options with Mathematical Models

5

This is an introductory course on options and other financial derivatives, and their applications to risk management. We will start with discrete-time, binomial trees models, but most of the course will be in the framework of continuous-time, Brownian Motion driven 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. You should have a working knowledge of basic calculus, statistics, and probability and be interested in the use of mathematical modeling. Please go to Unit 0 in the Course Outline to take the prerequisites assessment.

Galaxies and Cosmology

4.3

Class Central TipsLearn How to Sign up to Coursera courses for free1600+ Coursera Courses That Are Still Completely FreeThis class is an introduction to the modern extragalactic astronomy and cosmology, i.e., the part of astrophysics that deals with the structure and evolution of the universe as a whole, and its major constituents: dark matter, dark energy, galaxies, quasars, large-scale structure, and intergalactic gas.  It will cover the subjects including: relativistic cosmological models and their parameters, extragalactic distance scale, cosmological tests, composition of the universe, dark matter, and dark energy; the hot big bang, cosmic nucleosynthesis, recombination, and cosmic microwave background; formation and evolution of structure in the universe; galaxy clusters, large-scale structure and its evolution; galaxies, their properties and fundamental correlations; formation and evolution of galaxies; star formation history of the universe; quasars and other active galactic nuclei, and their evolution; structure and evolution of the intergalactic medium; diffuse extragalactic backgrounds; the first stars, galaxies, and the reionization era.  It corresponds to the Ay 21 class taught at Caltech.

Principles of Economics with Calculus

4.2

This course provides a quantitative and model-based introduction to basic economic principles, and teaches how to apply them to make sense of a wide range of real world problems. Examples of applications include predicting the impact of technological changes in market prices, calculating the optimal gasoline tax, and measuring the value of new products. This is a real Caltech class. It will be taught concurrently to Caltech and on-line students. This has two implications. On the costs side: the class is challenging, makes extensive use of calculus, and will demand significant effort. On the benefit side: successful completion of the class will provide you with an in-depth understanding of basic economics, and will permanently change the way you see the world.

The Evolving Universe

4

Class Central TipsLearn How to Sign up to Coursera courses for free1600+ Coursera Courses That Are Still Completely FreeThis is an introductory astronomy survey class that covers our understanding of the physical universe and its major constituents, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole.

The Evolving Universe

0

This is an introductory astronomy survey class that covers our understanding of the physical universe and its major constituents, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole. We will learn how modern astronomical observations and applications of physics we know from the planet Earth reveal the nature of these objects and explain their observed properties, and tell us how they form and evolve. We will also examine various cosmic phenomena, from variable or exploding stars to the expansion of the universe and the evidence for dark matter, dark energy, and the big bang. The universe as a whole and all of its major constituents are evolving, and we now have a fairly complete and consistent picture of these processes that is based on the objective evidence from observations and the laws of physics. The goal of this class is both to learn about the fascinating objects and phenomena that populate the universe, and to understand how we know all that.

Pricing Options with Mathematical Models

0

Class Central TipsLearn How to Sign up to Coursera courses for free1600+ Coursera Courses That Are Still Completely FreeThis 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.