Hedging and Evaluating Tail Risks via Two Novel Options Based on Type II Extreme Value Distribution
Hedging and Evaluating Tail Risks via Two Novel Options Based on Type II Extreme Value Distribution
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DOI：
10.3390/sym13091630
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Hang Lin;Lixin Liu;Zhengjun Zhang
中科院分区：
文献类型：
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作者：
Hang Lin;Lixin Liu;Zhengjun Zhang
尾部风险是当今重要的金融问题，但由于不容易指定合适的和不对称的定价核，因此使用特设期权直接对冲尾部风险仍然是一个未解决的问题。本文通过定义两种特设标的资产，设计了两种新的尾部风险期权（TRO）来对冲和评估短期尾部风险。在最大损失的Fréchet分布假设下，得到了封闭形式的TRO定价公式。仿真算例验证了定价公式的准确性。此外，他们表明，无论是在规模水平（对称的“正常”风险，具有更大的波动性）或形状水平（不对称的尾部风险，具有较小的值在尾部指数），风险越大，越昂贵的TRO电话，和便宜的TRO卖。使用校准，可以获得TRO隐含波动率和TRO隐含尾部指数。前者类似于Black-Scholes隐含波动率，可以度量市场整体的对称波动率。后者衡量基础损失的不对称性，反映市场情绪，并提供金融危机预警。关于新提出的TRO及其隐含的尾部指数，可以为投资者、投资组合经理和政策制定者提供经济含义。
Tail risk is an important financial issue today, but directly hedging tail risks with an ad hoc option is still an unresolved problem since it is not easy to specify a suitable and asymmetric pricing kernel. By defining two ad hoc underlying “assets”, this paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks. Under the Fréchet distribution assumption for maximum losses, the closed-form TRO pricing formulas are obtained. Simulation examples demonstrate the accuracy of the pricing formulas. Furthermore, they show that, no matter whether at scale level (symmetric “normal” risk, with greater volatility) or shape level (asymmetric tail risk, with a smaller value in tail index), the greater the risk, the more expensive the TRO calls, and the cheaper the TRO puts. Using calibration, one can obtain the TRO-implied volatility and the TRO-implied tail index. The former is analogous to the Black-Scholes implied volatility, which can measure the overall symmetric market volatility. The latter measures the asymmetry in underlying losses, mirrors market sentiment, and provides financial crisis warnings. Regarding the newly proposed TRO and its implied tail index, economic implications can be offered to investors, portfolio managers, and policy-makers.