Abstract
Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in-the-money and out-of-the-money) of time-to-maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface.
| Original language | English |
|---|---|
| Pages (from-to) | 804-824 |
| Number of pages | 21 |
| Journal | Applied Stochastic Models in Business and Industry |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2016 Nov 1 |
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Business, Management and Accounting(all)
- Management Science and Operations Research
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The Heston model with stochastic elasticity of variance. / Choi, Sun Yong; Kim, Jeong-Hoon; Yoon, Ji Hun.
In: Applied Stochastic Models in Business and Industry, Vol. 32, No. 6, 01.11.2016, p. 804-824.Research output: Contribution to journal › Article
TY - JOUR
T1 - The Heston model with stochastic elasticity of variance
AU - Choi, Sun Yong
AU - Kim, Jeong-Hoon
AU - Yoon, Ji Hun
PY - 2016/11/1
Y1 - 2016/11/1
N2 - Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in-the-money and out-of-the-money) of time-to-maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface.
AB - Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in-the-money and out-of-the-money) of time-to-maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface.
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U2 - 10.1002/asmb.2203
DO - 10.1002/asmb.2203
M3 - Article
VL - 32
SP - 804
EP - 824
JO - Applied Stochastic Models in Business and Industry
JF - Applied Stochastic Models in Business and Industry
SN - 1524-1904
IS - 6
ER -