A delay financial model with stochastic volatility; martingale method

作者：Lee Min Ku; Kim Jeong Hoon; Kim Joocheol

来源：Physica A: Statistical Mechanics and Its Applications , 2011, 390(16): 2909-2919.

DOI：10.1016/j.physa.2011.03.032

• Black-Scholes formula
• Delay
• Stochastic volatility
• Martingale
• Option pricing

In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results.

• 出版日期2011-8-15