Joint survival probability via truncated invariant copula

Kim, Jeong Hoon; Ki, Yong; Park, Chan Yeol

doi:10.1016/j.chaos.2016.01.012

Cited by 4 publications

(5 citation statements)

References 12 publications

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“…For example, our result can easily be applied to perturbed Gaussian copula and to the valuation of FX quanto options to a third currency. Also, this result can provide a very useful guide for credit risk management (refer to [9] and [10]). We leave these issues as future research topics.…”

Section: Final Remarksmentioning

confidence: 92%

Analytic approximation of the transition density function under a multi-scale volatility model

Ma¹

2017

HJMS

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The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. We propose an approach which can be used for the analytic approximation of the transition density related to a multi-scale stochastic volatility model. Using perturbation theory, we compute the leading-order term and the first-order correction terms. A numerical test also confirms the effectiveness of the model.

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Section: Final Remarksmentioning

confidence: 92%

Analytic approximation of the transition density function under a multi-scale volatility model

Ma¹

2017

HJMS

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“…This paper offers various possible directions for further development. This result can provide a very useful guide for credit risk management (see [13,[15][16][17]). We leave these issues as future research topics.…”

Section: Final Remarksmentioning

confidence: 95%

“…By multiplying (15) with ε and then letting ε tend to zero, we obtain the ordinary differential equation (ODE)…”

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confidence: 99%

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Correlated Log-Normal Random Variables under a Multiscale Volatility Model

2021

Advances in Mathematical Physics

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The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded by deriving the numerical results that further validate the effectiveness of the model.

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“…Our result can be applied to pricing and hedging spread options and is to incorporate a slowly varying volatility-driving process into the SFMR model. Also, this result can provide a very useful guide for credit risk management (see [26,27]). We leave these issues as future research topics.…”

Section: Final Remarksmentioning

confidence: 99%

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

2017

Advances in Mathematical Physics

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The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie-Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.

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Joint survival probability via truncated invariant copula

Cited by 4 publications

References 12 publications

Analytic approximation of the transition density function under a multi-scale volatility model

Analytic approximation of the transition density function under a multi-scale volatility model

Correlated Log-Normal Random Variables under a Multiscale Volatility Model

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

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