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

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

2008-06-05

arxiv.org/abs/0806.0932v1

Phys. Rev. E 78, 016101 (2008).

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

10.1103/PhysRevE.78.016101

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.

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