SVI 303 · Tier 300 — Advanced — Stochastic & Volatility · 3 credits
Risk-Neutral Density & Probability
Breeden–Litzenberger: turning option prices into the probability distribution the RND Mountain renders, and reading its moments.
Prerequisites
Learning Objectives
- State the Breeden–Litzenberger result and derive the risk-neutral density as the discounted second strike-derivative of the call price.
- Read a risk-neutral density as a PDF and integrate it into a CDF to answer probability questions about where price lands.
- State the Bakshi-Kapadia-Madan result: risk-neutral variance, skewness, and kurtosis as price-weighted integrals of the out-of-the-money option strip.
- Define the risk-neutral CDF from a density and explain why inverting it answers 'which strike has probability p of finishing in-the-money'.
- Explain why simulating from the market's implied risk-neutral density is different from, and more honest than, simulating from a fitted lognormal.