Local Volatility in Terms of Implied Volatility

Local volatility surface corresponding to the implied volatility surface

Loosely speaking:

• Local volatility is the instantaneous volatility at time T if the spot is S at that time.

• Implied volatility is the expected integrated volatility from today up to time T if the spot ends up at S at that time.

1. Lecture 1: Stochastic Volatility and Local Volatility

2. Derivation of Local Volatility

   1. Note that there is a typo in the article In Dupire's paper, why is (𝑆𝑡,𝑡) in the (𝐾,𝑇) space?

3. 21-256: Implicit partial differentiation