TY - GEN
T1 - Implied volatility of basket options at extreme strikes
AU - Gulisashvili, Archil
AU - Tankov, Peter
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function.
AB - In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function.
KW - Basket options
KW - Copula
KW - Implied volatility asymptotics
KW - Index options
KW - Large/ small strikes
KW - Time change
UR - https://www.scopus.com/pages/publications/84969233426
U2 - 10.1007/978-3-319-11605-1_6
DO - 10.1007/978-3-319-11605-1_6
M3 - Conference contribution
AN - SCOPUS:84969233426
SN - 9783319116044
T3 - Springer Proceedings in Mathematics and Statistics
SP - 175
EP - 212
BT - Large Deviations and Asymptotic Methods in Finance
A2 - Friz, Peter K.
A2 - Gatheral, Jim
A2 - Gulisashvili, Archil
A2 - Teichmann, Josef
A2 - Friz, Peter K.
A2 - Jacquier, Antoine
PB - Springer New York LLC
T2 - Workshop on Large Deviations and Asymptotic Methods in Finance, 2013
Y2 - 9 April 2013 through 11 April 2013
ER -