Quadratic hedging with multiple assets under illiquidity with applications in energy markets
Quadratic hedging with multiple assets under illiquidity with applications in energy markets
复制标题
流动性不足的情况下多种资产的二次对冲及其在能源市场的应用
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Meyer
中科院分区：
文献类型：
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作者：
Panagiotis;Nils Detering;T. Meyer
当流动性受到关注并且交易受交易成本影响时，我们建议对一般或有债权采取对冲方法。多种不同流动性水平的资产可用于对冲。我们的风险标准旨在最大限度地降低股价波动风险和降低流动性成本之间的权衡。遵循 \c{C}etin U.、Jarrow R.A. 和 Protter P. (2004) 的观点，我们在无套利环境中工作，假设每种资产都有供给曲线。在离散时间内，遵循 Schweizer M. (1998) 和 Lamberton D.、Pham H.、Schweizer M. (1998) 的思想，我们证明了在价格过程的温和条件下存在局部风险最小化策略。在随机和时间相关的流动性风险下，我们在线性供给曲线模型的情况下给出了最优策略的封闭式解。最后，我们展示了如何将我们的对冲方法应用于可以交易不同期限的期货的能源市场。最接近交割期的期货通常是最具流动性的，但根据或有债权，在对冲方面不一定是最佳的。在模拟研究中，我们研究了这种权衡，并将所得的对冲策略与经典策略进行了比较。
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and incurring low liquidity costs. Following \c{C}etin U., Jarrow R.A., and Protter P. (2004) we work in an arbitrage-free setting assuming a supply curve for each asset. In discrete time, following the ideas in Schweizer M. (1998) and Lamberton D., Pham H., Schweizer M. (1998) we prove the existence of a locally risk-minimizing strategy under mild conditions on the price process. Under stochastic and time-dependent liquidity risk we give a closed-form solution for an optimal strategy in the case of a linear supply curve model. Finally we show how our hedging method can be applied in energy markets where futures with different maturities are available for trading. The futures closest to their delivery period are usually the most liquid but depending on the contingent claim not necessary optimal in terms of hedging. In a simulation study we investigate this tradeoff and compare the resulting hedge strategies with the classical ones.