Ternary Regime Switching Modelling for Financial Asset Price Data

Abstract

In this project a ternary regime Markov switching jump diffusion model for financial asset price data is proposed. Initially, we propose a statistical technique for the detection of jumps and volatility estimation in a return time series data using a threshold method. As the threshold and volatility estimator are derived together by solving an implicit equation, this leads to unprecedented accuracy in jump detection over wide-ranging parameter values. Next, using the proposed threshold method the increments attributed to jumps are removed from historical data of various Indian sectoral indices. Thereafter, we attempt to model the derived continuous part of the data by analysing the presence of regime switching dynamics in the volatility coefficient using discriminating statistics, proposed by us, which are sensitive to the transition kernel of the regime switching model.In particular we have restricted ourselves to ternary regime switching dynamics. Finally, the performance of the proposed regime switching model is tested by examining its replication of the empirical Cumulative Distribution Function(eCDF) of the return time series.