TY - JOUR
T1 - Short Maturity Forward Start Asian Options in Local Volatility Models
AU - Pirjol, Dan
AU - Wang, Jing
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019
Y1 - 2019
N2 - We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behavior when the strike is extremely large, small, or close to the initial price of the underlying asset.
AB - We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behavior when the strike is extremely large, small, or close to the initial price of the underlying asset.
KW - Asian option
KW - Finance
KW - large deviations
KW - local volatility model
KW - short maturity asymptotics
KW - variational problems
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U2 - 10.1080/1350486X.2019.1584533
DO - 10.1080/1350486X.2019.1584533
M3 - Article
AN - SCOPUS:85070445114
SN - 1350-486X
VL - 26
SP - 187
EP - 221
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
IS - 3
ER -