I was woundering whether the option implied probability density of the logreturns:

$x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ?

I was asking myself this question because we model the "randomness" in the logreturn with a Brownian motion which is symmetric around zero, which leads to a model of the form:

$dx_T = a(x,t)dt+b(x,t)dW_T$ with $W_T$ the Brownian motion. Where we simply have a drift where we superimpose a random walk.

In this kind of model there can't be a skewness, now I was woundering whether there were any models which take skewness into account and if it's already been seen in the disstribution of the logreturns ?

I was wondering whether the option implied probability density of the log returns:

$x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ?

I was asking myself this question because we model the "randomness" in the log return with a Brownian motion which is symmetric around zero, which leads to a model of the form:

$dx_T = a(x,t)dt+b(x,t)dW_T$ with $W_T$ the Brownian motion. Where we simply have a drift where we superimpose a random walk.

In this kind of model there can't be a skewness, now I was wondering whether there were any models that take skewness into account and if it's already been seen in the distribution of the log returns?

I was woundering whether the option implied probability density of the logreturns:

$x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ?

I was woundering about it and I believe it should be because in every model (that I've seen so far) we model the "randomness" with a Brownian motion which is symmetric around zero, which leads to a model of the form:

$dx_T = a(x,t)dt+b(x,t)dW_T$ with $W_T$ the Brownian motion. Where we simply have a drift where we superimpose a random walk. But that's just what I'm thinking, since I'm quite new to the subject I can't be sure.

I was woundering whether the option implied probability density of the logreturns:

$x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ?

I was asking myself this question because we model the "randomness" in the logreturn with a Brownian motion which is symmetric around zero, which leads to a model of the form:

$dx_T = a(x,t)dt+b(x,t)dW_T$ with $W_T$ the Brownian motion. Where we simply have a drift where we superimpose a random walk.

In this kind of model there can't be a skewness, now I was woundering whether there were any models which take skewness into account and if it's already been seen in the disstribution of the logreturns ?