Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform

Jiling Cao, Xi Li and Wenjun Zhang ()
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Jiling Cao: Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand
Xi Li: Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand
Wenjun Zhang: Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand

JRFM, 2023, vol. 16, issue 10, 1-17

Abstract: In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation.

Keywords: asymptotic approximation; barrier; down-and-out; floating strike; lookback; Mellin transform; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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