Implied Volatility, the Smile and Volatility Trading

If the Black-Scholes model were right, every option on the same underlying and expiry would have the same implied volatility. In real markets they do not. Plotted against strike, implied volatilities form a smile or a skew, and plotted against strike and expiry they form a surface that traders build, fit and watch every day.

How is implied volatility calculated?

There is no formula for it. You take the market price of an option and solve the Black-Scholes formula backwards for the volatility that reproduces it, using a numerical method such as Newton’s method. The course covers the method, the data cleaning that real quotes need, and the cases where the solver fails.

What makes a volatility surface arbitrage-free?

Option prices must be consistent with each other: prices across strikes must imply non-negative probabilities, and total variance must not fall as expiry lengthens. A surface fitted carelessly can break these conditions and allow risk-free profits on paper. You will test your own fitted surface against them.

Why does implied volatility usually exceed realized volatility?

Volatility trading treats the size of market moves as something to buy and sell. An option-holder who hedges the direction away is left with a bet on volatility: profit if the market moves more than the option price implied, loss if it moves less. This course teaches how that works, the instruments desks use, and the risks that have broken funds.

Because investors pay for insurance against crashes, and sellers of that insurance demand a premium for the losses they take in them. That gap, the volatility risk premium, has been one of the most persistent sources of return in markets, and one of the most dangerous to collect without limits.

Who is this course for?

Options traders, volatility analysts and quant developers who build or use volatility surfaces.

What you will be able to do

• Compute implied volatility from option prices with a root-finding method.
• Describe the equity skew and the currency smile and explanations for each.
• Build a volatility surface from market quotes.
• Fit a parametric surface such as SVI and check it for arbitrage.
• Explain local volatility in outline and what it implies for pricing.
• Explain and measure the profit of a delta-hedged option from implied and realized volatility.

Syllabus, module by module

1. Implied volatility

   Inverting Black-Scholes, Newton and bisection methods, and data cleaning.

2. The smile and skew

   Patterns by asset class, the post-1987 equity skew and the explanations offered.

3. Term structure

   Volatility by expiry, event volatility and forward volatility.

4. Realized and implied volatility

   Estimators of realized volatility and what implied volatility forecasts.

5. The delta-hedged option

   Gamma, theta and the profit from the gap between implied and realized.

What every course contains

Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.

1. Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
2. Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
3. Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
4. Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
5. Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
6. Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
7. Transcript. A full transcript of every film and every audio recording, searchable and quotable.
8. Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
9. Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
10. Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.

How the certificate is earned

An assessed project: you build an implied volatility surface from a day of option quotes, fit a parametric model, test it for arbitrage, and submit the code with a report. On a pass you receive the Course certificate in Implied Volatility, the Smile and Volatility Trading, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. Read how certification works.

Before you start

This course assumes the material of the courses below, or the same knowledge gained elsewhere.

• The Black-Scholes Model and the Option Greeks