Pricing regime-switching risk in an HJM interest rate environment

Elliott, Robert J.; Siu, Tak Kuen

doi:10.1080/14697688.2015.1136078

Cited by 14 publications

(3 citation statements)

References 45 publications

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“…This list is merely indicative and not exhaustive. Some other works involving hidden Markov models of asset price, can be found in References 11 and 12, and references therein. Since the MMGBM market model is incomplete, the fair price of a derivative is not unique.…”

Section: Introductionmentioning

confidence: 99%

Regime recovery using implied volatility in Markov modulated market model

Goswami

Mukherjee

Patalwala

et al. 2022

Appl Stoch Models Bus & Ind

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In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered the locally risk minimizing theoretical price of European vanilla options.By pretending these prices or their numerical approximations as traded prices, we have first computed the implied volatility (IV) of the underlying asset. Then by performing several numerical experiments on ternary regime models we have investigated the dependence of IV on the time to maturity (TTM) and strike price of the vanilla options. We have observed a clear dependence that is at par with the empirically observed stylized facts. Furthermore, we have experimentally validated that IV time series, obtained from contracts with moneyness and TTM varying in a particular narrow range, can recover the transition instances of the hidden Markov chain having three states. Such regime recovery for any arbitrary state-space and transition parameters has also been established in a theoretical setting. Moreover, the novel scheme for computing option price is shown to be stable.

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Section: Introductionmentioning

confidence: 99%

Regime recovery using implied volatility in Markov modulated market model

Goswami

Mukherjee

Patalwala

et al. 2022

Appl Stoch Models Bus & Ind

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“…Hence, Gray in [15] models the short interest rate as a discrete regimeswitching process. Elliott and Siu [12] proposed a model of term structure of interest rates in a Markovian, regime-switching Health-Jarrow-Morton framework. Zhang et al [26] showed the existence of stationary distribution of CIR process with Markov switching under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching

Hou

Shao

2019

Sci. China Math.

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This work is denoted to studying the tail behavior of Cox-Ingersoll-Ross (CIR) processes with regime-switching. One essential difference shown in this work between CIR process with regime-switching and without regime-switching is that the stationary distribution for CIR process with regime-switching could be heavy-tailed. Our results provide a theoretical evidence of the existence of regime-switching for interest rates model based on its heavy-tailed empirical evidence. In this work, we first provide sharp criteria to justify the existence of stationary distribution for the CIR process with regime-switching, which is applied to study the long term returns of interest rates. Then under the existence of the stationary distribution, we provide a criterion to justify whether its stationary distribution is heavy-tailed or not.

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“…The main goal of this article is to introduce the second Kummer function with matrix parameters and to study its asymptotic behaviour. This function appears as a solution of an equation in mathematical finance, where a Markovian regime switching framework (see [8,9] as an example) is combined with an equilibrium model for asset bubbles from [10,11]. In such a model, knowing the asymptotic behaviour of the solution is essential.…”

Section: Introductionmentioning

confidence: 99%