Heston Stochastic Volatility Model and Fast Fourier Transforms
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I am a huge Carr-Madan enthusiast, it was an honor to discuss this work. I'll never forget the time I first learned of Fourier inversion techniques for pricing, I was sitting on a QR desk that was previously headed by Peter Carr and a senior quant mentioned this seminal work - I was hooked immediately! I'm never certain how much interest there is about my personal experiences academically and professionally as a quant - I tend to stick to the quant material itself. Depending on interest perhaps this will change at some point!
I hope you enjoyed the video!
Roman
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📖 Chapters:
00:00 - Introduction
02:50 - Understanding Option Pricing
09:04 - Beyond Black-Scholes: Heston Model
12:24 - Problems Pricing Options with a Heston Model
13:41 - Understanding Fourier Transforms
16:19 - Example: Discrete (Fast) Fourier Transform
18:42 - Example: Inverse Discrete (Fast) Fourier Transform
19:23 - Understanding Characteristic Functions
20:41 - Putting All of the Pieces Together
23:50 - Understanding Option Pricing via Fourier Inversion (Carr-Madan)
28:56 - The Breakthrough Connection
31:08 - Why it Works and Guidelines for Coding Implementation
33:13 - Heston FFT Pricing Code and Discretization Errors
35:41 - Closing Thoughts and Future Topics
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