Pricing of contingent convertibles under smile conform models
Pricing of contingent convertibles under smile conform models
复制标题
微笑符合模型下的或有敞篷车的定价
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
W. Schoutens
中科院分区：
文献类型：
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作者：
J. M. Corcuera;Jan De Spiegeleer;Albert Ferreiro;A. Kyprianou;D. Madan;W. Schoutens
我们看看CoCo债券的定价问题，其中潜在的风险资产动态是由一个微笑符合模型，更准确地说，一个指数列维过程，包括跳跃和重尾。为了生成CoCo价格的精确分析表达式，需要以封闭形式的核心数学量是固定时间的基础股票价格过程的下确界定律。除了带漂移的布朗运动外，在Levy过程类中还没有适合于金融建模的封闭解析形式。然而最近有一些显着的进展与理论的一个大家庭的利维过程，称为β-过程，比照。Kuznetsov [12] and Kuznetsov et al. [14].事实上，对于这类Levy过程，在一个独立的、指数分布的随机时间下确界的定律可以用其特征指数的根和极点来表示;所有这些都很容易在复平面的一个轴上的规则间隔沿着内找到。将这些结果与最近由Kuznetsov等人提出的蒙特-卡罗技术结合在一起。[13]，该技术利用了下确界的随机律，我们展示了CoCos的高效和有效的数值定价。我们使用一类特殊的β-过程进行分析，称为β-VG，它与经典的方差-Gamma模型具有相似的特性。该理论是通过执行两个案例研究。在根据市场数据校准我们的模型后，我们对其中一个劳埃德CoCo和第一个Rabo CoCo进行了定价和分析。
We look at the problem of pricing CoCo bonds where the underlying risky asset dynamics are given by a smile conform model, more precisely an exponential Levy process incorporating jumps and heavy tails. A core mathematical quantity that is needed in closed form in order to produce an exact analytical expression for the price of a CoCo is the law of the infimum of the underlying equity price process at a fixed time. With the exception of Brownian motion with drift, no such closed analytical form is available within the class of Levy process that are suitable for financial modeling. Very recently however there has been some remarkable progress made with the theory of a large family of Levy processes, known as β-processes, cf. Kuznetsov [12] and Kuznetsov et al. [14]. Indeed for this class of Levy processes, the law of the infimum at an independent and exponentially distributed random time can be written down in terms of the roots and poles of its characteristic exponent; all of which are easily found within regularly spaced intervals along one of the axes of the complex plane. Combining these results together with a recently suggested Monte-Carlo technique, due to Kuznetsov et al. [13], which capitalises on the randomised law of the infimum we show the efficient and effective numerical pricing of CoCos. We perform our analysis using a special class of β-processes, known as β-VG, which have similar characteristics to the classical Variance-Gamma model. The theory is put to work by performing two case studies. After calibrating our model to market data, we price and analyze one of the Lloyds CoCos as well as the first Rabo CoCo.
关于 Lamperti 稳定过程
DOI：
10.48550/arxiv.0802.0851
发表时间：
2008
期刊：
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影响因子：
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作者：
Caballero M
通讯作者：
Caballero M