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摘要翻译：
我们为股票、政府债券、公司债券和衍生品的同时建模提出了一个通用框架。不确定性是由一般的仿射马尔可夫过程产生的。这种设置允许随机波动、跳跃、违约的可能性以及不同资产之间的相关性。我们通过求解一个耦合的广义Riccati方程组来计算折现复矩。这就产生了一种计算电力收益价格的有效方法。欧洲的看涨和看跌期权以及二进制期权和资产或无资产期权可以用Carr和Madan(1999)和Lee(2005)的快速傅立叶变换方法定价。其他欧洲收益可以用政府债券、电力收益和普通期权的线性组合来近似。我们表明，结果优于只使用政府债券和权力收益或政府债券和普通期权。本文还给出了当足够多的金融工具可变现时，欧洲大陆债权可复制的条件，并研究了动态套期保值策略。作为一个例子，我们讨论了一个具有违约可能性和随机利率的Heston型随机波动率模型。
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英文标题：
《Pricing and Hedging in Affine Models with Possibility of Default》
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作者：
Patrick Cheridito, Alexander Wugalter
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最新提交年份：
2011
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分类信息：
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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英文摘要：
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the possibility of default and correlation between different assets. We show how to calculate discounted complex moments by solving a coupled system of generalized Riccati equations. This yields an efficient method to compute prices of power payoffs. European calls and puts as well as binaries and asset-or-nothing options can be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005). Other European payoffs can be approximated with a linear combination of government bonds, power payoffs and vanilla options. We show the results to be superior to using only government bonds and power payoffs or government bonds and vanilla options. We also give conditions for European continent claims in our framework to be replicable if enough financial instruments are liquidly tradable and study dynamic hedging strategies. As an example we discuss a Heston-type stochastic volatility model with possibility of default and stochastic interest rates.
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PDF链接：
https://arxiv.org/pdf/1012.0754
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