TY - JOUR
T1 - Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility
AU - Figueroa-López, José E.
AU - Ólafsson, Sveinn
N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.
AB - In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.
KW - ATM option pricing
KW - Exponential Lévy models
KW - Implied volatility
KW - Short-time asymptotics
KW - Stochastic volatility models
UR - https://www.scopus.com/pages/publications/84953836439
U2 - 10.1007/s00780-015-0281-z
DO - 10.1007/s00780-015-0281-z
M3 - Article
AN - SCOPUS:84953836439
SN - 0949-2984
VL - 20
SP - 219
EP - 265
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 1
ER -