Equity-linked annuities with multiscale hybrid stochastic and local volatility

Sun Yong Choi, Jeong Hoon Kim

Research output: Contribution to journalArticle

Abstract

In recent times, hybrid underlying models have become an industry standard for the pricing of derivatives and other problems in finance. This paper chooses a hybrid stochastic and local volatility model to evaluate an equity-linked annuity (ELA), which is a sort of tax-deferred annuity whose credited interest is linked to an equity index. The stochastic volatility component of the hybrid model is driven by a fast mean-reverting diffusion process while the local volatility component is given by the constant elasticity of variance (CEV) model. Since contracts of the ELA usually have long maturities over 10 years, a slowly moving factor in the stochastic volatility of stock index is expected to play a significant role in the valuation of the ELA, and thus, it is added to the aforementioned model. Based on this multiscale hybrid model, an analytic approximate formula is obtained for the price of a European option in terms of the CEV probability density function and then the result is applied to the value of the point-to-point ELA. The formula leads to the dependence structure of the ELA price on the fast and slow scale stochastic volatility and the elasticity of variance.

Original languageEnglish
Pages (from-to)466-487
Number of pages22
JournalScandinavian Actuarial Journal
Volume2016
Issue number5
DOIs
Publication statusPublished - 2016 May 27

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Equity
Volatility
Stochastic Volatility
Hybrid Model
Elasticity
European Options
Stock Index
Multiscale Model
Dependence Structure
Tax
Finance
Valuation
Diffusion Process
Probability density function
Sort
Pricing
Stochastic volatility
Local volatility
Annuities
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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

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Equity-linked annuities with multiscale hybrid stochastic and local volatility. / Choi, Sun Yong; Kim, Jeong Hoon.

In: Scandinavian Actuarial Journal, Vol. 2016, No. 5, 27.05.2016, p. 466-487.

Research output: Contribution to journalArticle

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