A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

Abstract

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our new analytical formulas are tested with numerical Monte Carlo simulations.

References in corpus (3)

• Scaling of the distribution of fluctuations of financial market indices
• A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
• Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes

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• Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
• Quantum effects in an expanded Black-Scholes model
• Path Integral and Asian Options