Path integral pricing of outside barrier Asian options

Path integral pricing of Wasabi option in the Black–Scholes model

“…That the solution to the path integral (8) is also the fundamental solution to (9) is basically the content of the celebrated Feynman-Kac theorem [15]. Define the propagator W P (X T , T, λ|X 0 , 0) for a driftless risky asset X t that spends λ unit of time over the constant level b…”

“…Therefore the need for closed-forms or computationally inexpensive approximation has always been a driving force in the field and should remain so in the foreseeable future. Since its emergence among econophysicists' toolbox, which can be traced back to the seminal work from Dash [4] [5] and Linetsky [6], the path integral framework has proved to be especially well suited [7][8] [9] to the study of exotic options. On a historic note, the path integral itself was developed by Wiener [10] [11] as a way to do computation on Brownian paths, and later on by Feynman [12] for its original description of quantum mechanics.…”