Detection of high and low states in stock market returns with MCMC method in a Markov switching model

Dynamics of Tokyo Electric Power Company and the Nikkei: 1985 to 2016 including the Fukushima disaster

“…The parameters of the Markov-switching model are obtained with a Bayesian Markov chain Monte Carlo estimation, based on Gibbs sampling. Hahn et al (2010) and Rey et al (2014) present a technical explanation of this method. Balcilar et al (2015) select this approach to study the response of stock prices to a shock in oil prices in an MS-VEC model.…”

“…However, the standard deviations increase strongly in the high-volatility regime, with stronger responses than in the low-volatility regime. This distinction might arise because high-volatility regimes generally characterize periods in which large changes occur in the asset rates of return, upward or downward (Rey et al 2014). Figure 8 plots the impulse responses to a shock in TEPCO returns.…”

The Probabilistic Genotyping Software STRmix: Utility and Evidence for its Validity

“…MCMC is a widely used technique and is considered a mainstream statistical tool. It is used in real estate market prediction (41), earthquake and rock fracturing (42), electricity capacity modeling (43), weather prediction (44), betting (45), climate (46), computational biology (47), computational linguistics (48), genetics (49), engineering (50), physics (51), aeronautics (52), stock market prediction (53), and social science (54). The key papers describing the algorithms used within the MCMC are Metropolis et al (55), with 37,506 cites in Google Scholar (as at May 27, 2018), and Hastings (56), with 12,229 cites providing some measure of their widespread acceptance and use.…”

Connection between trinomial trees and finite difference methods for option pricing with state-dependent switching rates

“…Since at the terminal time t n ≡ T the FDM value equals the true option value, we know that Ψ n is a zero vector. Therefore (28) follows from (36) using ∆t = T /n. Now we prove (29).…”

“…They are first introduced by Hamilton [16] and have had many applications in finance including equity options [2,5,7,8,11,13,14,17,20,24,26,32,35,36,12,27,18], bond prices [23] and interest rate derivatives [3,25], portfolio selection [39], trading rules [10,33,34,37,38] , and others. There are many empirical studies on the Markov regime switching models (see e.g., [9], [15], [28], [4] and the references therein), which make the models popular and usable.…”