TY - JOUR
T1 - Asymptotics for the discrete-Time average of the geometric Brownian motion and Asian options
AU - Pirjol, Dan
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
Copyright © Applied Probability Trust 2017Â.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-Time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-Time averaging in the Black-Scholes model, with both fixed and floating strike.
AB - The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-Time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-Time averaging in the Black-Scholes model, with both fixed and floating strike.
KW - Asian option
KW - Berry-Esseen bound
KW - central limit theorem
KW - large deviations
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U2 - 10.1017/apr.2017.9
DO - 10.1017/apr.2017.9
M3 - Article
AN - SCOPUS:85021374246
SN - 0001-8678
VL - 49
SP - 446
EP - 480
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 2
ER -