1997/08/22 by Belal E. Baaquie, B. E. Baaquie · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Stochastic processes and financial applications #cond-mat #hep-th
paper · pdf · doi:10.1051/jp1:1997167
Needs subeqnarray.sty. To appear in J. de Phys. I (Dec 97)
arxiv created 1997/08/22 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrodinger wavefuction of quantum mechacnics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived. 1