Practitioner course in derivatives
Implied Volatility and the Volatility Smile
What option prices say about expected volatility: solving for implied volatility, the smile and skew, the term structure, building and fitting a volatility surface, and the no-arbitrage conditions a surface must satisfy.
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.
Who is this course for?
Options traders, volatility analysts and quant developers who build or use volatility surfaces. It counts toward the Certificate in Derivatives Pricing.
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.
Syllabus, module by module
Implied volatility
Inverting Black-Scholes, Newton and bisection methods, and data cleaning.
The smile and skew
Patterns by asset class, the post-1987 equity skew and the explanations offered.
Term structure
Volatility by expiry, event volatility and forward volatility.
The surface
Strike, moneyness and delta coordinates; interpolation and extrapolation.
Parametric fits
The SVI parameterisation and fitting it to quotes.
No-arbitrage conditions
Calendar and butterfly arbitrage and how to test a surface for them.
Local volatility
Dupire's formula in outline and the smile dynamics it implies.
Project lab
Supervised work on the assessed surface project.
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, issued by the Institute with a verification code. Read how certification works.
Before you start
The material of The Black-Scholes Model and Option Greeks, and working Python.
This course counts toward
Questions applicants ask
What is implied volatility?
The volatility that, put into the Black-Scholes formula, gives the option’s market price. It is the market’s price for volatility, expressed in a common unit, rather than a direct forecast.
Why is there a volatility smile?
Because the Black-Scholes assumptions do not hold: returns have fat tails, volatility changes and tends to rise when prices fall, and investors pay extra for crash protection. In equity markets the smile has been a pronounced skew since the 1987 crash.