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?

  • $\begingroup$ Check out this, this or this other questions. $\endgroup$ Commented Jul 25, 2018 at 15:05
  • $\begingroup$ 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. $\endgroup$
    – Quantuple
    Commented Jul 26, 2018 at 7:24


Browse other questions tagged or ask your own question.