Laughter in the Dark: An Introduction to the Volatility Smile

 

Lips (Heure de l'Observatoire)

Man Ray

 

These are unpublished lecture notes from the Master's in Financial Engineering Program at Columbia University. I have used many published papers and books to improve (I hope) the pedagogic nature of these notes, and perhaps not referenced them properly. Since they are in rough form, I will be pleased to correct any errors or omissions. I'll add new lectures as the semester progresses. Note that some lectures don't manage to cover all the topics listed in the title during the class time alloted, in which case that material is continued in the following lecture.

Lectures
Lecture 1: The Principles of Valuation
Lecture 2: Dynamic Replication: Myths and Realities of Options Pricing
Lecture 3: The Smile: Constraints and Problems
Lecture 4: Arbitrage Bounds, Problems with Valuation, Models
Lecture 5: Static Hedging and Implied Distributions
Lecture 6: Extending Black Scholes & Local Volatility Models
Lecture 7: More about Local Volatility Models
Lecture 8: Implications of Local Volatility Models
Lecture 9: Regimes of Volatility
Lecture 10: Stochastic Volatility Models of the Smile
Lecture 11: More on Stochastic Volatility Models of the Smile
Lecture 12: Jump Diffusion Models of the Smile
Lecture 13: Conclusions