Simulation of Stochastic Volatility using Path Integration: Smiles and Frowns

2000/08/23 by Belal E. Baaquie, Baaquie, Belal E., L. C. Kwek +3 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed Matter (cond-mat) #FOS: Physical sciences #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/0008327

Needs graphicx.sty and mathfont.sty; 11 gif files and 14 encapsulated postscript files (figures)

arxiv created 2000/08/23 · openalex publication_date 2000/08/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of path integration. Using market data, we determine the parameters of the model. It is found that the market chooses a special class of models for which a more efficient algorithm, called the bisection method, is applicable. Using our simulated data, we generate some implied volatility curves. We also analyze and study in detail some of the characteristics of the volatility curves within the model.

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