非高斯收益下Delta套期保值期权的定价
Delta Hedged Option Valuation with Underlying Non-Gaussian Returns
摘要：
将标准的Black-Scholes期权定价理论推广到由一般概率分布描述的潜在收益波动情形。设计了一个Langevin过程及其相关的Fokker-Planck方程来模拟市场的随机动力学，从而使我们能够写出并正式求解动态套期保值所隐含的广义Black-Scholes方程。然后，围绕一个非扰动的起点进行系统的扩展，恢复Matacz的固定期权定价表达式。我们执行的应用程序，我们的形式主义，真正的股票市场，并找到明确的证据表明，虽然过去的金融时间序列可以用来评估期权价格到期日之前，具有合理的准确性，波动率的随机特性是一个必不可少的成分，必须考虑到分析期权价格建模。
英文摘要：
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generalized Black-Scholes equation implied by dynamical hedging. A systematic expansion around a non-perturbative starting point is then implemented, recovering the Matacz's conjectured option pricing expression. We perform an application of our formalism to the real stock market and find clear evidence that while past financial time series can be used to evaluate option prices before the expiry date with reasonable accuracy, the stochastic character of volatility is an essential ingredient that should necessarily be taken into account in analytical option price modeling.
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