My Finance

We still need to make changes to our simulator in light of our very recent research:

1. Replace volatility in the autoregression with its Box-Cox transform. This will model the volatility as the classic autoregression of order 1 with Gaussian IID innovations. Update: we need Yeo-Johnson transform because Box-Cox is valid only for positive values. In this new post, we discussed that Yeo-Johnson transform works for log volatility values, and enables us to apply objective Bayes inference for autoregression coefficients. Update: We did not simulate correlated innovations, as discussed here. We need to correct this.
2. Edit total returns of 10-year zero-coupon bonds to update equations and account for noise. This will not improve much, but it is important for completeness and intellectual honesty. We will have 9 equations with 9 noise series. Update: we used total returns of 7-year zero-coupon Treasury bonds instead of 10-year zero-coupon Treasury bonds. They fit better because they have IID Gaussian regression residuals without the need of any transforms. And they have more data, going back to 1962.
3. Add the intercept to the regression of (modified) corporate bond returns vs changes in the rate (which shows duration); this will help to make it classic simple linear regression. Regression residuals are still IID Gaussian. I think we did not include the intercept to stress the meaning of the duration. Update: We were successful, see this GitHub repository.
4. Update the covariance and the correlation matrix of residuals. They will both be of size 9. Update: We only need the covariance matrix, see item 5 below.
5. Add the Bayesian-full (not Bayesian-lite) option to the classic (frequentist) option. We did not add Bayesian-lite because we found there is not much difference between the two Bayesian versions. Update: As shown by simulations of simple models for a single stock asset class and a single volatility factor, Bayesian-lite and Bayesian-full are very close but quite different from the frequentist mode. Therefore, we use Bayesian-lite not Bayesian-full, since it is much easier to fix the point estimate of the entire covariance matrix of innovations, and then use objective Bayes inference for coefficients. Update: We did not simulate correlated innovations, as discussed here. We need to correct this.
6. Later we add the following options: Instead of this full version, remove dependence of all three stock returns upon bond duration, valuation measure, and risk spread. Or pick any combination of 3 factors for each stocks. Update: It would be great to code regression fit inside the simulator, otherwise we will need to manually code each and every covariance matrix. This has many shortcomings: (a) It can introduce manual errors. (b) It would take a lot of time. (c) When we change model or data so slightly, even just updating this for one year, we will need to update the entire model, which can lead to (a) or (b). Update: We found, to our shock, there is no loss in runtime. Moreover, 100 or 10000 Monte Carlo simulations? this does not matter for the runtime!
7. In the above item, check that each version has Gaussian IID residuals, and add Bayesian-full version. Update: We only need the Bayesian-lite version, see item 5 above.

Total 8 versions in item 6, times 2 in item 7, so 16 versions. We could have more options, but let us keep it simple for now. And do not forget to add explicit initial values of the four market factors. Do not write a separate advanced version of the simulator. Fix the current values of these market factors as default ones. But users must see them explicitly and be able to change them.