I want to simulate a credit spread index which is negatively correlated to a given random walk of a stock index. They should be correlated in such a way that larger than average stock growth tend to tighten spreads, and lower than average growth tends to increase spreads.
One idea I have is \begin{equation} \text{spread}(t) = \alpha - \beta*(R(t) - R) + \epsilon(t), \end{equation} with $\alpha>0$, $\beta>0$, $\epsilon(t)$ a gaussian distribution, $R(t)$ the stock return (or drift) and $R$ the average stock return. This relation is obviously inspired by CAPM, but with some important modifications. One problem with this model is negative spreads when the return is of order $\alpha / \beta$.
I am wondering whether this is the right approach, or whether another approach is adviced. To emphasize: I want to keep it simple. Of course I know the relation between stock prices and credits is more complex, but the negative correlation with a random element suits my purpose.
Thank you in advances!
