Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering

Kou, Steven

doi:10.1016/s0927-0507(07)15002-7

Cited by 86 publications

(56 citation statements)

References 72 publications

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“…But the main weakness of this model is that for the jump-diffusion system [3] with stochastic intensity, the process evolution is difficult to track, which also made the parameter calibration really complicated. In order to reduce the complexity and make the process tractable, we investigate the bankrupt stocks, which are definitely hard-to-borrow.…”

Section: Further Discussion Of the Htb Modelmentioning

confidence: 99%

Dynamics of Bankrupt Stocks

Lipkin

Sowers³

2014

SIAM J. Finan. Math.

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In this thesis, we study the behavior of bankrupt stocks. Bankrupt stock is a special case of the Hard-to-Borrow stocks. Besides the general nice feature of the Hard-to-borrow feedback for the buy-in demand, the bankrupt stocks could exclude the diffusive effects. This nice property would modify the Marco Avellaneda and Mike Lipkin's jump-diffusion model for the Hard-to-Borrow stocks into the pure jump systems with stochastic intensity. Under this main assumption, our model is a two-dimensional integrate-and-fire model which is recursively tractable. By investigating the dynamics of the model, we could capture the self-reinforcing aspect of the buy-ins and subsequent crashes of the stock price.Having the recursively explicit dynamics of the stock prices and buy-in rate on hand, we can calibrate the model under the physical measure by error minimization. One way to justify the fit of the calibration results is to compare the sample path and the real prices.On the other hand, we match the option pricing theory against observed behavior of the options to see how the periodic buy-ins would act to cover the the cost of the short position, which gives the mechanism of the essential feedback of the Hard-to-Borrowness.

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Section: Further Discussion Of the Htb Modelmentioning

confidence: 99%

Dynamics of Bankrupt Stocks

Lipkin

Sowers³

2014

SIAM J. Finan. Math.

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“…An example of such model is the generalized Black-Scholes model, where jump-process behavior is described with a Poisson process [9].…”

Section: Advances In Computer Science Research (Acsr) Volume 72mentioning

confidence: 99%

SDE Simulation in One Click: Fiction or Reality?

Barysheva¹,

Markov²

2017

Proceedings of the IV International Research Conference "Information Technologies in Science, Management, Social Sphere and Med

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-Stochastic differential equations (further referred to as SDEs) and the models based on SDE are widely used to describe stochastic processes in virtually any area of human activity, such as biology or finance. Unlike an analytical approach to solving SDE, the simulation methods allow to significantly increase the range of practical problems, which examples are given in the paper. Capture III describes the result of the comparative analysis of existing programming tools for SDE simulation, their advantages and shortcomings. It was shown that none of the existing tools completely meet the requirements formulated in Chapter III for the tool's functionality used for building a simulation model.

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“…In other words, they handle short-term smiles better. Kou (2002Kou ( , 2007 showed that the addition of jump in the Black-Scholes model generates high peak (under-reaction) in the asset return leptokurtic distribution and heavy tails (over-reaction). In his paper, Merton (1976) assumed that the extra randomness of the underlying asset price due to jumps can be diversified away.…”

Section: Public Interest Statementmentioning

confidence: 99%

Evaluation of variable annuity guarantees with the effect of jumps in the asset price process

Juma

Lee

Chin

et al. 2017

Cogent Economics & Finance

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Financial crisis in [2007][2008] have caused losses to life insurance companies issuing variable annuities with guarantees. This is partly due to failure of variable annuity (VA) issuers to anticipate the large variations in asset prices during the financial crisis times in their pricing framework and also setting a higher guaranteed rate. This study aims to investigate the pricing of the guaranteed minimum death and accumulation benefits embedded in flexible premium VA. We compare the prices from calibrated Black-Scholes model to that of calibrated jump-diffusion model. Although both models assume constant volatility, the fact that Black-Scholes model ignores abnormal asset price changes due to jumps is likely to under-price the VA. We also conduct a case study to analyse the impact on guarantee fees for different stock market performance and regional mortality rates.

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Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering

Abstract: In this survey we shall focus on the following issues related to jump-diffusion models for asset pricing in financial engineering.

Cited by 86 publications

References 72 publications

Dynamics of Bankrupt Stocks

Dynamics of Bankrupt Stocks

SDE Simulation in One Click: Fiction or Reality?

Evaluation of variable annuity guarantees with the effect of jumps in the asset price process

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