Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach
Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach
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DOI：
10.1016/j.rinam.2022.100353
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发表时间：
2022-05
影响因子：
2
通讯作者：
Y. Ota;Yu Jiang;Daiki Maki
中科院分区：
文献类型：
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作者：
Y. Ota;Yu Jiang;Daiki Maki
无套利性质为金融衍生产品的定价提供了一种简单的方法。然而，套利机会存在于各个领域，即使是很短的时间。通过了解套利属性的存在，我们可以采取金融交易策略。研究了金融市场中具有适当初始条件的倒向抛物型方程的逆期权问题。我们确定了这个问题的系数从测量数据，并试图找到套利机会，在金融市场上使用贝叶斯推理方法，这是作为IOP解决方案。参数的后验概率密度函数由测量数据计算。未知参数的统计估计马尔可夫链蒙特卡罗（MCMC）算法，它利用后验状态空间。MCMC算法的有效采样策略使我们能够通过贝叶斯推理技术解决反问题。我们的数值结果表明，贝叶斯推断方法可以同时估计未知的趋势和波动系数从人工测量数据和真实的金融市场数据。
No-arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist in various fields, even for a very short time. By knowing that an arbitrage property exists, we can adopt a financial trading strategy. This paper investigates the inverse option problems (IOP) in the backward parabolic equation with a suitable initial condition in financial markets. We identify the coefficients of this problem from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the artificial measured data and the real financial market data.