Abstract
The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance (CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].
| Original language | English |
|---|---|
| Pages (from-to) | 611-622 |
| Number of pages | 12 |
| Journal | Acta Mathematicae Applicatae Sinica |
| Volume | 32 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2016 Jul 1 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
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A delayed stochastic volatility correction to the constant elasticity of variance model. / Lee, Min Ku; Kim, Jeong Hoon.
In: Acta Mathematicae Applicatae Sinica, Vol. 32, No. 3, 01.07.2016, p. 611-622.Research output: Contribution to journal › Article
TY - JOUR
T1 - A delayed stochastic volatility correction to the constant elasticity of variance model
AU - Lee, Min Ku
AU - Kim, Jeong Hoon
PY - 2016/7/1
Y1 - 2016/7/1
N2 - The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance (CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].
AB - The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance (CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].
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U2 - 10.1007/s10255-016-0588-3
DO - 10.1007/s10255-016-0588-3
M3 - Article
AN - SCOPUS:84983266482
VL - 32
SP - 611
EP - 622
JO - Acta Mathematicae Applicatae Sinica
JF - Acta Mathematicae Applicatae Sinica
SN - 0168-9673
IS - 3
ER -