Surmount GausSAR

2021年10月4日

Overview
The Surmount GausSAR is a simplified version of an idea to extend the basic Gaussian model by allowing for endogenous regime switching. Conditional on a given regime, the distribution of price changes is multivariate normal.
However, when the endogenous regimes are integrated out, it becomes a mixture of Gaussian distributions.

Concepts
This approach accommodates heavy tails, persistence, and nonlinear dynamics. More precisely, let k = 1,…, K denote the admissible regimes and Zt with values in {1,…, K} denote the market regime at date t. It is assumed that
(Zt) is a Markov chain with transition matrix Q.
The distribution of price changes Δpt conditional on
Zt=k,Δpt_,Zt_
is multivariate normal N[μk,Ωk.
Then the conditional distribution of price changes is
(4.11)
l(Δpt|Δpt-1_)=∑k=1kpk(Δpt-1_)N(μk,Ωk),
where
pk(Δpt-1_)=P[Zt=k|Δpt-1_].
.
Probabilities pk can be computed numerically and parameters μk, Ωk, ∀k and Q can be estimated by means of the Kitagawa's algorithm. Then, the conditional VaR is estimated from drawings in the mixture distribution after replacing pk, μk, Ωk by their estimates.
This approach is different from the mixture of normal distributions proposed by J.P. Morgan as a new methodology of VaR computation. Under the J.P. Morgan approach, the regime indicators (Zt) are assumed time independent.

How To Use
The indicator has been color coded to make for quick & easy visual understanding.
Put simply:
Green = Bullish
Purple = Decreasing Bullish-ness or Neutral
Orange = Bearish
Yellow = Decreasing Bearish-ness or Neutral

It’s also useful to pay attention to the trajectory of the indicator where, put simply:
+ 0 increasing away from mean (0) = Bullish
+ 0 decreasing towards mean (0) = Decreasing Bullish-ness
0 = Essentially neutral, but pay attention to the most recent trend
- 0 decreasing away from mean (0) = Bearish
- 0 increasing towards mean (0) = Decreasing Bearish-ness


Thank you for the support! We look forward to providing some more indicators that can hopefully make a positive impact on traders’ comfort within the markets & understanding of technical indicators.