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!

  • $\begingroup$ You could try a logistic regression model for the probability of default with such a setup, and then calculate a credit spread from that (if you know the recovery rate) $\endgroup$ Oct 12, 2022 at 18:12


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