Bayesian analysis of contingent claim model error
Bayesian analysis of contingent claim model error
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DOI：
10.1016/s0304-4076(99)00020-2
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发表时间：
2000
影响因子：
6.3
通讯作者：
Eric Jacquier;R. Jarrow
中科院分区：
文献类型：
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作者：
Eric Jacquier;R. Jarrow
本文将参数不确定性和模型误差正式引入未定权益模型的实现中。我们对误差的分布做了假设，以允许使用与参数不确定性和模型误差一致的基于似然的估计。然后，我们写了一个贝叶斯估计，不依赖于大样本的属性，但允许精确的推断的相关功能的参数（期权价值，对冲比率）和预测。这一点至关重要，因为频繁更新模型参数的常见做法导致样本量较小。即使对于简单的误差结构和Black-Scholes模型，贝叶斯估计也没有解析解。马尔可夫链蒙特卡罗估计有助于解决这个问题。我们展示了它们如何扩展到错误结构的一些概括。我们应用这些估计的Black-Scholes。鉴于最近的工作使用非参数函数来定价期权，我们嵌套的B-S在其输入的多项式展开。尽管改进了样本内拟合，但扩展并没有产生比B-S更好的样本外改善。此外，样本外误差虽然大于样本内误差，但幅度相同。这与流行的隐含树方法的性能形成对比，隐含树方法产生出色的样本内拟合，但灾难性的样本外拟合，如大仲马，Fleming和Whaley（1997）所示。这意味着估计方法与模型本身一样重要。
This paper formally incorporates parameter uncertainty and model error into the implementation of contingent claim models. We make hypotheses for the distribution of errors to allow the use of likelihood based estimators consistent with parameter uncertainty and model error. We then write a Bayesian estimator which does not rely on large sample properties but allows exact inference on the relevant functions of the parameters (option value, hedge ratios) and forecasts. This is crucial because the common practice of frequently updating the model parameters leads to small samples. Even for simple error structures and the Black–Scholes model, the Bayesian estimator does not have an analytical solution. Markov chain Monte Carlo estimators help solve this problem. We show how they extend to some generalizations of the error structure. We apply these estimators to the Black–Scholes. Given recent work using non-parametric function to price options, we nest the B–S in a polynomial expansion of its inputs. Despite improved in-sample fit, the expansions do not yield any out-of-sample improvement over the B–S. Also, the out-of-sample errors, though larger than in-sample, are of the same magnitude. This contrasts with the performance of the popular implied tree methods which produce outstanding in-sample but disastrous out-of-sample fit as Dumas, Fleming and Whaley (1997) show. This means that the estimation method is as crucial as the model itself.