What sort of qualitative behaviour does a stock following a process of the form $dS_t=α(μ-S_t )dt+S_t \sigma dW_t$ exhibit? The following is a question taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, Exercise $5.5$

Question: What sort of qualitative behaviour does a stock following a process of the form 
  $$dS_t=α(μ-S_t )dt+S_t \sigma dW_t$$
  exhibit? What qualitative effects do altering $μ$ and $α$ have? What effects do they have on the price of a call option?

My attempt:
Assume that $\alpha>0.$ If $S_t<\mu,$ then $\alpha(\mu-S_t)>0.$ 
Similarly, if $S_t>\mu,$ then $\alpha(\mu-S_t)<0.$
This means that if $\alpha>0,$ then $S_t$ is mean-reverting. 
Conversely, if $\alpha<0,$ similar analysis above implies that $S_t$ is trend following. 
In the derivation of Black-Scholes call option price, mean rate of a geometric Brownian motion does not affect the price as it will be changed into risk-free rate. 
As the volatility is the same, $\alpha$ and $\mu$ do not have any effect on the price of a call option.
Is my reasoning above correct? 
 A: You are right about the mean-reverting feature. A couple of things to add. The parameter $\mu$ is the long run level of the stock price and $\alpha$ is the speed of the adjustment towards the long run level. It's difficult to believe that a stock has a fixed long run level since stock prices tend to increase with time, so this model is not used for equity options. The mean reverting feature is usually used in interest rate models (like Hull and White, Vacicek model, etc.) where you consider a long run  interest rate. For $\alpha > 0 , \mu >0,$ $S_t$ is always positive. This is another reason why the mean reverting feature used to be popular to model interest rates. But it's not longer the case since now you can see negative interest rate in the markets.
For you second question, I don't think your answer is right. This SDE is different from B-S SDE and has a different solution. The unique solution is
$$S_t = S_0 \exp[-(\lambda + \sigma^2 / 2)t + \sigma W_t] + \lambda \mu \int_0^t \exp[-(\lambda + \sigma^2 /2 )(t-s) + \sigma(W_t-W_s)]ds.$$ 
You can check that the above equation is a solution by using Ito's lemma and then check that the drift and diffusion coefficients satisfy Lipschitz and linear growth conditions to conclude that the solution is unique. By looking at the solution is clear that $S_T$ is not log-normal distributed as in B-S model. Since the models are different, it doesn't make sense to input a B-S volatility in this model. We would have to find first a formula for a call option and calibrate the parameters. Then for the same option, we would get a different $\sigma$ that the one in B-S model. There is no analytical formula for a call option when S follows this SDE anyway. 
