论文标题
向后SPDE的粗略波动下的定价选项
Pricing Options Under Rough Volatility with Backward SPDEs
论文作者
论文摘要
在本文中，我们研究了粗糙波动率模型的期权定价问题。由于该框架是非马克维亚人，因此欧洲选项的价值函数不是确定性的。相反，它是随机的，可以满足向后的随机部分微分方程（BSPDE）。对于具有无界的随机领导系数的一般非线性BSPDE的弱解的存在和唯一性也证明了其与某些前向后的随机微分方程的连接也被得出了。然后将这些BSPDE用于近似美国期权价格。还研究了一种基于倾斜的方法，以实现此类BSPDE和相关的非马克维亚定价问题的数值近似值。最后，针对欧美期权计算了粗糙的伯戈米类型的例子。
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial differential equation (BSPDE). The existence and uniqueness of weak solution is proved for general nonlinear BSPDEs with unbounded random leading coefficients whose connections with certain forward-backward stochastic differential equations are derived as well. These BSPDEs are then used to approximate American option prices. A deep leaning-based method is also investigated for the numerical approximations to such BSPDEs and associated non-Markovian pricing problems. Finally, the examples of rough Bergomi type are numerically computed for both European and American options.
