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“…Such a model can be regarded as a simple type of stochastic volatility model, in which the stochastic driver of the volatility is a Markov chain instead of the Brownian motion which is traditionally used for stochastic volatility models, such as the models of Hull and White, of Stein and Stein and of Heston or the SABR model. Option pricing in regime-switching diffusion models is attracting an increasing interest in the literature: we mention [4] as an early reference, and as more recent ones [7], [9], [17], [18], [19], [24], [35], [37].…”

confidence: 99%

“…Such a model can be regarded as a simple type of stochastic volatility model, in which the stochastic driver of the volatility is a Markov chain instead of the Brownian motion which is traditionally used for stochastic volatility models, such as the models of Hull and White, of Stein and Stein and of Heston or the SABR model. Option pricing in regime-switching diffusion models is attracting an increasing interest in the literature: we mention [4] as an early reference, and as more recent ones [7], [9], [17], [18], [19], [24], [35], [37].…”

confidence: 99%

“…Hybrid models driven by finite-state Markovian chains have also been increasingly employed as suitable models for modelling uncertainty in modern economic or financial systems (see, e.g., [6,14,15,16]). The hybrid models randomly switch between finite number of regimes in anticipation to unexpected abrupt structural changes in underlying economic or financial mechanisms.…”

confidence: 99%

“…Example 1.1. The first model we want to discuss is constant elasticity of variance (CEV) model with Markov switching [6]. Suppose that the price process S(t) of the risky asset S evolves over time according to the following stochastic differential equation with regime-switching dS(t) = µ(β(t))S(t)dt + σ(β(t))S θ (t)dW (t), S(0) = s > 0, (1.1) where W (•) is a standard Brownian motion, β(•) is a Markov chain with finite state space M, µ(i 0 ) and σ(i 0 ) ≥ 0, i 0 ∈ M, are the appreciation rate and the volatility of the risky asset S at time t, respectively, and 0 < θ < 1 is the constant elasticity parameter.…”

confidence: 99%