A jump to default extended CEV model: an application of Bessel processes
A jump to default extended CEV model: an application of Bessel processes
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DOI：
10.1007/s00780-006-0012-6
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发表时间：
2006-08
影响因子：
1.7
通讯作者：
P. Carr;V. Linetsky
中科院分区：
文献类型：
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作者：
P. Carr;V. Linetsky
我们开发了一个灵活且易于分析的框架，该框架统一了公司负债、信用衍生品和股票衍生品的估值。我们假设股票价格遵循扩散，其间可能跳到零(默认)。为了捕捉违约和股票波动性之间的正向联系，我们假设违约率是标的股票回报的瞬时方差的递增仿射函数。为了捕捉波动性和股价之间的负联系，我们假设违约前的瞬时股票波动率是一个恒定的方差弹性(CEV)规范。我们证明了时间和规模的确定性变化将我们的股票价格过程归结为一个标准的带杀戮的Bessel过程。这种削减允许开发完全显式的封闭形式的解决方案，用于风险中性生存概率、CDS利差、公司债券价值和欧式股票期权。此外，我们的估值模型非常灵活，可以对其进行校准，以精确匹配任意给定的CDS利差、利率、股息收益率和现金隐含波动率的期限结构。
We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.