论文标题
在马尔可夫调制市场模型中使用隐含波动率的政权恢复
Regime recovery using implied volatility in Markov modulated market model
论文作者
论文摘要
在资产价格动力学的黑色choles-Merton模型的政权切换扩展中，人们假设波动系数将演变为隐藏的纯跳跃过程。在马尔可夫政权转换的假设下，我们考虑了欧洲香草期权价格的局部风险。通过假装这些价格或它们作为交易价格的嘈杂版本，我们首先计算了基础资产的隐含波动性（IV）。然后，通过执行几个数值实验，我们研究了IV对成熟时间（TTM）的依赖性和香草选项的罢工价格。我们已经观察到与经验观察到的风格化事实相当的明显依赖性。此外，我们已经在实验上验证了IV时间序列，从金钱和TTM的合同中获得的iV时间序列尤其狭窄的范围可以恢复隐藏的马尔可夫链的过渡实例。这种政权恢复也已在理论环境中得到了证明。此外，计算期权价格价格的新颖方案显示为稳定。
In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered the locally risk minimizing price of European vanilla options. By pretending these prices or their noisy versions as traded prices, we have first computed the implied volatility (IV) of the underlying asset. Then by performing several numerical experiments we have investigated the dependence of IV on the time to maturity (TTM) and strike price of the vanilla options. We have observed a clear dependence that is at par with the empirically observed stylized facts. Furthermore, we have experimentally validated that IV time series, obtained from contracts with moneyness and TTM varying in particular narrow ranges, can recover the transition instances of the hidden Markov chain. Such regime recovery has also been proved in a theoretical setting. Moreover, the novel scheme for computing option price is shown to be stable.
