Heston-Type Stochastic Volatility with a Markov Switching Regime

Elliott, Robert J.; Nishide, Kazuhiko; Osakwe, Carlton

doi:10.2139/ssrn.2470975

Cited by 3 publications

(20 citation statements)

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“…Despite large differences in computational time, the results of the three methods are very close. This is in contrast to the results of Elliott et al (), in which, however, only the two classical computational methods were considered. Furthermore, they only considered maturities up to 1 year, and in their numerical results, it appears that the difference between Monte Carlo prices and those based on the semianalytic formula increases with maturity.…”

Section: Introductioncontrasting

confidence: 91%

“…In this paper, we are able to extend the arguments from El Euch and Rosenbaum (), as well as from Elliott et al (), to derive an analytic representation of the Laplace functional of the asset price. By Fourier inversion, semianalytic pricing formulae for put and call options are given.…”

Section: Introductionmentioning

confidence: 88%

“…Thus our regime switching rough Heston model will inherit the analytic tractability of the rough Heston model, which was derived in El Euch and Rosenbaum (, ), and the tractability of the regime switching extension the Heston model as in Elliott et al (). Two important stylized features of volatility, namely, the (locally) rough behavior, and the regime switching property consistent with more long‐term economic considerations, are accommodated in one consistent model approach.…”

Section: Introductionmentioning

confidence: 93%

“…We now incorporate a regime switching into the mean‐reversion level

θ

as in Elliott et al () and merge this with the rough volatility model above. This leads to the following stochastic integral equation for

V

V_{t} - V_{0} = \frac{κ}{normalΓ (α)} \int_{0}^{t} {(t - s)}^{α - 1} (θ_{s} - V_{s}) d t + \frac{σ}{normalΓ (α)} \int_{0}^{t} {(t - s)}^{α - 1} \sqrt{V_{s}} d W_{s},

where

W

is now a standard Brownian motion having correlation

ρ

with

B

and

{(θ_{s})}_{0 \leq t < \infty}

is a finite state, time‐homogeneous Markov process with generator matrix

Q

independent of

S

and

W

.…”

Section: Basic Model Descriptionmentioning

confidence: 99%

“…Another stream of research, as described in Elliott, Chan, and Siu () and Elliott, Nishide, and Osakwe (), argues that the asset price dynamics or the associated volatility process exhibits regime changes. For example, the empirical analysis of Maghrebi, Holmes, and Oya () comes to the conclusion that the model should have at least two regimes under the risk‐neutral measure.…”

Section: Introductionmentioning

confidence: 99%

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Regime switching rough Heston model

Alfeus

Overbeck

Schlögl

2019

Journal of Futures Markets

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This model combines two important stylized features of volatility, the rough behavior consistent with a Hurst parameter less than 0.5, and the regime switching property consistent with more long‐term economic considerations. It is nevertheless highly tractable in the sense of semianalytic formulae for European options, and permits a partial Monte Carlo method of similar computational speed as the semianalytic formula (at an appropriate number of Monte Carlo simulations). While option prices are relatively insensitive to the choice of Hurst parameter, introducing rough volatility allows for a better fit to the at‐the‐money skew.

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Section: Introductioncontrasting

confidence: 91%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 93%

“…We now incorporate a regime switching into the mean‐reversion level

θ

as in Elliott et al () and merge this with the rough volatility model above. This leads to the following stochastic integral equation for

V

V_{t} - V_{0} = \frac{κ}{normalΓ (α)} \int_{0}^{t} {(t - s)}^{α - 1} (θ_{s} - V_{s}) d t + \frac{σ}{normalΓ (α)} \int_{0}^{t} {(t - s)}^{α - 1} \sqrt{V_{s}} d W_{s},

where

W

is now a standard Brownian motion having correlation

ρ

with

B

and

{(θ_{s})}_{0 \leq t < \infty}

is a finite state, time‐homogeneous Markov process with generator matrix

Q

independent of

S

and

W

.…”

Section: Basic Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Regime switching rough Heston model

Alfeus

Overbeck

Schlögl

2019

Journal of Futures Markets

View full text Add to dashboard Cite

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Regime switching affine processes with applications to finance

et al. 2020

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We introduce the notion of a regime switching affine process. Informally this is a Markov process that behaves conditionally on each regime as an affine process with specific parameters. To facilitate our analysis, specific restrictions are imposed on these parameters. The regime switches are driven by a Markov chain. We prove that the joint process of the Markov chain and the conditionally affine part is a process with an affine structure on an enlarged state space, conditionally on the starting state of the Markov chain. Like for affine processes, the characteristic function can be expressed in a set of ordinary differential equations that can sometimes be solved analytically. This result unifies several semi-analytical solutions found in the literature for pricing derivatives of specific regime switching processes on smaller state spaces. It also provides a unifying theory that allows us to introduce regime switching to the pricing of many derivatives within the broad class of affine processes. Examples include European options and term structure derivatives with stochastic volatility and default. Essentially, whenever there is a pricing solution based on an affine process, we can extend this to a regime switching affine process without sacrificing the analytical tractability of the affine process. B M. van Beek

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