I am going to assume that you meant to ask how we can use option prices to inform trading of underlying stocks.

The Black-Scholes-Merton model says that under the physical measure, the underlying stock obeys a geometric Brownian motion: \begin{equation} dS*t = \mu S*t dt + \sigma S*t dZ*t. \end{equation} You can apply Ito's Lemma and integrate to obtain \begin{equation} S*t = S*0 \exp \left( \left( \mu - \frac{\sigma^2}{2} \right)t + \sigma Z*t \right). \end{equation} Now, $(Z*t)*{t \geq 0}$ is a standard Brownian motion under the physical measure. By definition, this means $Z*t \sim N(0, t)$. In other words, gross returns $R*{0,t} := \frac{S*t}{S*0}$ are distributed log normally; or, if you prefer, returns $r*{0,t} := ln S*t - ln S*0$ are distributed normally. **The first issue here is that this is a bad model for the behavior of returns on equity and equity indexes**. Whether you test for the normality of returns or for the log normality of gross returns, you will find that it is a bad model. Or, if you prefer, it's easy to find more flexible models that will be prefered from a Bayesian perspective, even if you use priors that favor this model.

However, the interest of the Black-Scholes-Merton model was not to describe the behavior of returns on equity as much as it was to provide a way to price European options. My favorite way of approaching this is to say that Girsanov's theorem tells you that the pricing kernel you should use is \begin{equation} m*t = m*0 \exp \left( - \int*0^t \theta*s ds - \frac{1}{2} \int*0^t \theta*s^2 ds \right) \end{equation} where $\theta*t := \frac{\mu - r}{\sigma}$ is your Sharp ratio. To be clear, this variable variable is chosen so that $m*t S*t$ and $m*t B*t$ (where $B*t$ would be the price of a riskless bond) are martingales under the physical measures. It so happens that $\exp(r \tau) m*t$ is a proper Radon-Nikodym derivative and you can use it to change to the risk-neutral measure: \begin{equation} C(t, t+\tau,, K, S*t) = E^P \left(m*{t+\tau} \left( S*{t+\tau} - K \right)*+ \right) = \exp(-r \tau) E^Q \left( \left( S*{t+\tau} - K \right)*+ \right). \end{equation} From those equations, you can derive the Black-Scholes-Merton formula. The martingale restriction in particular will impose that $S*t$ grows at a rate of $r$ rather than $\mu$ under $Q$ and Girsanov's theorem will tell you that a translated and scaled version of $Z_t$ is a standard Brownian motion under $Q$. With a bit of algebra, you would see that stock prices follow a geometric Brownian motion under $Q$ and you'd get an expression similar as that above for prices. From there, you'd exploit the log-normality of prices to compute the expectation under $Q$ and some tedious algebra later you would land on the famous Black-Scholes formula.

**The problem** with all of the above is that it relies on a lot of assumption, one of which says that the arbitrages you think you can find by trading stocks cannot exists... **But it might not be an insurmontable problem**.

If you assume that the Black-Scholes-Merton argument is "almost" correct in the sense that markets deviate temporarily from this and come back to it, you might be able to do something interesting. In particular, Black-Scholes-Merton gives you a direct link between **option prices** and **the conditional density of returns** under either measures. Even if the model is wrong, nothing forbids you to use the model to estimate the parameters $\mu, \sigma$ using option prices and plug that into a log-normal distribution to have a guess of where prices are likelier to land "sort of according to the derivative market."

**But, if you want to go in that direction, there might be better alternatives**. In particular, Breeden and Litzenberger (1978) gave us a way to related the risk-neutral density with option prices. Specifically, \begin{equation} f^Q(S*{t+\tau}, K) = \frac{\partial^2 C(t, t+\tau, K, S*t)}{\partial K^2}. \end{equation} This can approximated using a finite difference on a grid of strikes prices of options at time $t$, with all options maturing at time $t + \tau$. You pick the moment they mature according to whatever horizon you'd like to "forecast." Now, the twist here is that you have risk-neutral densities: this will mix information about changing risk compensations and changing expectations. However, nothing says you couldn't bet a machine learning algorithm with a suitable loss function couldn't use these as inputs and learn to provide you the information you need like a point forecast, an interval forecast, or quantile forecasts. The major advantage of the BL(1978) result is that it is as model-free as it will get and it allows you to use large cross-sections of options to say something potentially useful about the underlying.