The popularity of Bitcoin increases with time and investors take it as an alternative investment due to continuous financial instability and uncertainty throughout the world. It can be an alternative not only for developed markets but also for emerging and frontier markets. Prior to now, researchers focused solely on developed markets. For this purpose, the present paper has explored the answer to the question of whether Bitcoin enables a hedge or diversifier or safe-haven against emerging and frontier stock market indices. Instead of previous analyses, here we have examined constancy relationships as well as time-varying relationships between Bitcoin with four stock indices of emerging and frontier stock markets of four different countries. We have applied the GJR-GARCH method to find the answer to the question, and we have also applied the Threshold Autoregressive (TAR) model for cross-validation of the findings. Our empirical results have shown that Bitcoin has safe-haven abilities are in normal and turmoil market situations for emerging and frontier stock markets. Also, we have found evidence of hedging and diversification properties.