MCMC, Spot Volatility, and Strategic Value of Information
Spot Volatility
This is the major motivation for applying MCMC to smooth the noise part associated with the nonparametric estimation of spot volatility by fixing the local estimation window size. Traditionally, to obtain a relatively satisfactory estimation of spot volatility using nonparametric econometric tools, we need the asymptotic scheme, which is to some extent not that easy to be satisfied in practice for high-frequency trading since a lot of technical issues would be involved when we want to collect and sample data at high-frequency but maintain the number of observations reasonably large enough. This is the major motivation for applying MCMC to smooth noise part associated with the nonparametric estimation of spot volatility by fixing the local estimation window size (Bollerslev, Li and Liao ,2021).
Volatility and Strategic Value of Information
Kyle’s lambda as the measure bridging volatility and value of private information was intially proposed in Kyle (1985), later extended to continuous-timing setting in Back (1992) and more recently discussed in Back (2017). For more technical details and comprehensive discussions, please refer to the literature listed.
Idea is simple: Regression+Bayesian !!!
For Kyle’s lambda, using following regression to back out the slope as the target Kyle’s lambda.
Is Simple Regression Valid ? Almost Surely !!!

