TY - JOUR
T1 - Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion
AU - Pirjol, Dan
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/5
Y1 - 2023/5
N2 - We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion F(θ,T)=E[e−θXT] with [Formula Presented], which is exact in the limit σ2T→0 at fixed σ2θT2 and aT. This asymptotic result is applied to pricing zero coupon bonds in the Dothan model of stochastic interest rates. The asymptotic result provides an approximation for bond prices which is in good agreement with numerical evaluations in a wide range of model parameters. As a side result we obtain the asymptotics for Asian option prices in the Black-Scholes model, taking into account interest rates and dividend yield contributions in the σ2T→0 limit.
AB - We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion F(θ,T)=E[e−θXT] with [Formula Presented], which is exact in the limit σ2T→0 at fixed σ2θT2 and aT. This asymptotic result is applied to pricing zero coupon bonds in the Dothan model of stochastic interest rates. The asymptotic result provides an approximation for bond prices which is in good agreement with numerical evaluations in a wide range of model parameters. As a side result we obtain the asymptotics for Asian option prices in the Black-Scholes model, taking into account interest rates and dividend yield contributions in the σ2T→0 limit.
KW - Dothan model
KW - Geometric Brownian motion
KW - Large deviations
KW - Stochastic interest rates models
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U2 - 10.1016/j.orl.2023.04.002
DO - 10.1016/j.orl.2023.04.002
M3 - Article
AN - SCOPUS:85158904623
SN - 0167-6377
VL - 51
SP - 346
EP - 352
JO - Operations Research Letters
JF - Operations Research Letters
IS - 3
ER -