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Pricing and hedging of derivatives in contagious markets

机译：传染性市场中衍生产品的定价和对冲

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摘要

It is well documented that stock markets are contagious. A negative shock to one market increases the probability of adverse shocks to other markets. We model this contagion effect by including mutually exciting jump processes in the dynamics of the indexes' log-returns. On top of this we add a stochastic volatility component to the dynamics. It is important to take the contagion effect into account if derivatives written on a basket of assets are to be priced or hedged. Due to the affine model specification the joint characteristic function of the log-returns is known analytically, and for two specifications we detail how the model can be calibrated efficiently to option prices. In total we calibrate over an extended period of time the specifications to options data on four US stock indexes, and show how the models achieve satisfactory pricing errors. We study the effect of contagion on multi-asset derivatives prices and show how for certain derivatives the impact is heavy. Moreover, we derive hedge ratios for European put and call options and perform a numerical experiment, which illustrates the impact of contagious jumps on option prices and hedge ratios. Mutually exciting processes have been analyzed for multivariate intensity modeling for the purpose of credit derivatives pricing, but have not been used for pricing/hedging options on equity indexes. (C) 2016 Elsevier B.V. All rights reserved.
机译：众所周知，股市具有传染性。对一个市场的负面冲击增加了对其他市场的负面冲击的可能性。我们通过在索引的对数返回的动力学中包括相互激动的跳跃过程来模拟这种传染效应。最重要的是，我们在动态中添加了随机波动成分。如果要对一篮子资产上所写的衍生工具进行定价或对冲，则必须考虑到传染效应。由于仿射模型规格，对数收益率的联合特征函数在分析上是已知的，对于两个规格，我们详细介绍了如何有效地根据期权价格对模型进行校准。总的来说，我们将在很长一段时间内对四种美国股票指数的期权数据进行规范校准，并说明这些模型如何实现令人满意的定价误差。我们研究了蔓延对多资产衍生品价格的影响，并显示了对某些衍生产品的影响是巨大的。此外，我们得出了欧洲看跌期权和看涨期权的对冲比率，并进行了数值实验，该实验说明了传染性跳跃对期权价格和对冲比率的影响。为了进行信用衍生工具定价，已经对相互刺激的过程进行了多元强度建模的分析，但尚未用于股票指数的定价/对冲期权。 （C）2016 Elsevier B.V.保留所有权利。

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