A lattice model for option pricing under GARCH-jump processes

Lin, Bo‐Yen; Hung, Mao‐Wei; Wang, Jr‐Yan; Wu, Ping-Da

doi:10.1007/s11147-012-9087-8

Cited by 6 publications

(7 citation statements)

References 38 publications

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“…We make sure that the discounted asset dynamic is a martingale under the Q measure. This setting is consistent with Lin et al [21]. Similar to the definition of 𝑣 𝑡+1 in Eq.…”

Section: Corollary 21supporting

confidence: 91%

“…By incorporating the Poisson jump process and state-dependent volatility process, this model is general and complicated. If the parameters in variance equation do not rely on the realization of state, the model reduces to the GARCH-jump model in Lin et al [21]. If we drop the Poisson jump process, the model reduces to the RS-GARCH model in Chen and Hung [7].…”

Section: Corollary 21mentioning

confidence: 99%

“…, ±𝑛, 𝜂 𝑡 denotes the moving parameter, which is the smallest integer that makes sure that the probability of movement in each direction is between 0 and 1. Following Ritchken and Trevor [27] and Lin et al [21], we set…”

Section: Approximating the Rs-garch-jump Processmentioning

confidence: 99%

“…A small usually leads to more accuracy, but also results in more nodes and more computation time. To make a tradeoff between accuracy and efficiency, this study follows the suggestion of Lin et al [21] to set the space parameter as …”

Section: Approximating the Rs-garch-jump Processmentioning

confidence: 99%

“…Chen and Hung [7] proposed an -state Markov-switching GARCH option model and developed a new lattice algorithm to price options under this framework. Lin et al [21] combined the GARCH model with an additional jump process and developed a lattice model to value options. All these papers confirm that the lattice algorithm is an efficient and accurate numerical method in GARCH setting, thus we adopt the lattice algorithm and extend it to the RS-GARCH-jump framework.…”

Section: Introductionmentioning

confidence: 99%

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A lattice approach for option pricing under a regime-switching GARCH-jump model

Zhi-yu¹,

Bai²

2021

Prob. Eng. Inf. Sci.

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In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

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“…We make sure that the discounted asset dynamic is a martingale under the Q measure. This setting is consistent with Lin et al [21]. Similar to the definition of 𝑣 𝑡+1 in Eq.…”

Section: Corollary 21supporting

confidence: 91%

Section: Corollary 21mentioning

confidence: 99%