Replication Scheme for the Pricing of European Options
24 Pages Posted: 10 Mar 2019 Last revised: 18 Aug 2020
Date Written: February 7, 2019
This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.
Keywords: Local volatility model, stochastic volatility model, fractional volatlity model, chaos expansion, density matching, calibration
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