英文标题：
《Option Pricing in Markets with Unknown Stochastic Dynamics》
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作者：
Hanno Gottschalk, Elpida Nizami and Marius Schubert
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最新提交年份：
2017
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英文摘要：
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty of a market participant, we follow a Bayesian approach to option pricing. Here we use historic discrete or continuous observations of the market to set up posterior distributions for the future market. Given a subjective physical measure for the market dynamics, we derive the existence of arbitrage free pricing rules by constructing subjective option pricing measures. The non-uniqueness of such measures can be proven using the freedom of choice of prior distributions. The subjective market measure thus turns out to model an incomplete market. In addition, for the Black-Scholes market we prove that in the high frequency limit (or the long time limit) of observations, Bayesian option prices converge to the standard BS-Option price with the true volatility. In contrast to this, in the Merton market with normally distributed jumps Bayesian prices do not converge to standard Merton prices with the true parameters, as only a finite number of jump events can be observed in finite time. However, we prove that this convergence holds true in the limit of long observation times.
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中文摘要：
我们考虑Black-Scholes和Merton市场中欧式期权的无套利估值，其中市场的总体结构已知，但具体参数未知。为了反映市场参与者的这种主观不确定性，我们采用贝叶斯方法进行期权定价。在这里，我们使用对市场的历史离散或连续观察来建立未来市场的后验分布。给出市场动态的一个主观物理度量，通过构造主观期权定价度量，我们得到了无套利定价规则的存在性。这种测度的非唯一性可以用先验分布的自由选择来证明。因此，主观市场衡量标准被证明是一个不完全市场的模型。此外，对于Black-Scholes市场，我们证明了在观测的高频极限（或长时间极限）下，贝叶斯期权价格收敛于标准BS期权价格，且具有真实的波动性。与此相反，在具有正态分布跳跃的默顿市场中，贝叶斯价格不收敛于具有真实参数的标准默顿价格，因为在有限时间内只能观察到有限数量的跳跃事件。然而，我们证明了这种收敛在长观测时间的限制下是成立的。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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