# What is the risk neutral density and how is it estimated? [closed]

I don't understand the words "risk-neutral density". Please explain what it is, and how it can be estimated in practice.

My guess would be that we have an underlying probability space $(\Omega, P)$. We are interested in the equivalent martingale measure $Q$, i.e. the space $(\Omega, Q)$.

For every stock price $S_t$, we wish to determine the $Q$-distribution. The risk-neutral density, if it exists, is the density $\phi$ of $S_t$ with respect to the Lebesque measure, i.e. we can write for some fixed $t$, $$E^Q S_t = \int \phi \cdot s \ ds.$$

Is this guess correct? If so, how do we estimate $\phi$ from stock prices?

## closed as off-topic by Quantuple, LocalVolatility, Helin, Attack68♦, Bob Jansen♦Jul 31 '18 at 10:42

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – Quantuple, LocalVolatility, Helin, Attack68, Bob Jansen
If this question can be reworded to fit the rules in the help center, please edit the question.

• Check out this, this or this other questions. – Daneel Olivaw Jul 25 '18 at 15:05
• As Daneel Olivaw mentions with the "what" and the "how" in your questions have already been answered several times on this site. Please do some research next time. – Quantuple Jul 26 '18 at 7:24