No-arbitrage Approach to Pricing Credit Spread Derivatives
No-arbitrage Approach to Pricing Credit Spread Derivatives
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信用利差衍生品定价的无套利方法
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Kwok
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作者：
Chi Chiu;Chu And Yue;Kuen Kwok;Kuen Yue;Kwok
信用利差衍生品定价中的无套利是指通过拟合无违约债券和可违约债券价格的当前期限结构，确定瞬时即期利率和即期利差的均值回归随机过程中与时间相关的漂移项。在定价模型中，将参考实体的无风险利率和信用利差视为相关的随机状态变量。当即期汇率和即期价差均服从船体和白色模型时，可以推导出信用价差期权的时间依赖漂移项的解析表达式和价格解析公式。给出了信用利差衍生产品的数值估值算法，并研究了信用利差期权的定价行为。信用利差衍生工具是对信用利率敏感的金融工具，旨在对冲或利用参考实体（如风险债券）的信用利差变化。风险债券的信用利差是风险债券的当前收益率与可比到期日的基准利率之间的差额。利差代表市场对持有风险债券所要求的风险溢价。与违约掉期不同，信贷息差衍生工具不依赖于任何特定的信贷事件发生。信用价差期权的买方预先支付一笔溢价，作为回报，卖方同意支付一笔金额，如果实际的现货价差突破某个执行水平。或者，回报可能取决于两个参考实体的现货价差之间的差异。信用价差期权可以用来从期权溢价中赚取收入，赌一个人对信用价差变化的看法，或者以一个有利的价格在远期基础上购买一个参考实体。Jarrow，Lando，and Turnbull [1997]采用简化形式的方法，将违约事件建模为点过程，构建了一个马尔可夫链模型，用于风险债务和信用衍生品的估值，该模型将公司的信用评级作为违约可能性的指标。马尔可夫模型提供了一个无仲裁的信用利差期限结构的演变。在模型的数值实现中出现了问题，因为具有高信用评级的债券可能在样本期内没有违约，因此风险溢价调整变得不明确，因为估计的违约概率为零。Kijima和Komoribayashi [1998]提出了一种风险溢价技术。
No arbitrage in the case of pricing credit spread derivatives refers to determination of the time-dependent drift terms in the mean reversion stochastic processes of the instantaneous spot rate and spot spread by fitting the current term structures of default-free and defaultable bond prices. The riskless rate and the credit spread of a reference entity are taken to be correlated stochastic state variables in this pricing model. When the spot rate and spot spread both follow the Hull and White model, one can derive an analytic representation for the time-dependent drift terms and analytic price formulas for credit spread options. Algorithms for the numerical valuation of credit spread derivatives are developed, and the pricing behaviors of credit spread options are examined. C redit spread derivatives are credit rate-sensitive financial instruments designed to hedge against or capitalize on changes in the credit spread of a reference entity such as a risky bond. The credit spread of a risky bond is the difference between the current yield of the risky bond and a benchmark rate of comparable maturity. The spread represents the risk premium the market demands for holding the risky bond. Unlike default swaps, credit spread derivatives do not depend upon any specific credit event occurring. The buyer of a credit spread option pays an up-front premium, and in return the writer agrees to pay an amount should the actual spot spread breach some strike level. Alternatively, the payoff may depend on the difference between the spot spreads of two reference entities. Credit spread options may be used either to earn income from the option premium, to bet one's view on credit spread change, or to target the purchase of a reference entity on a forward basis at a favored price. By following a reduced-form approach that models the occasion of default as a point process, Jarrow, Lando, and Turnbull [1997] construct a Markov chain model for valuation of risky debt and credit derivatives that incorporates the credit ratings of a firm as an indicator of the likelihood of default. The Markov model provides the evolution of an arbitrage-free term structure of the credit spread. Problems arise in numerical implementation of the model because bonds with high credit ratings may experience no default within the sample period, so the risk premium adjustments become ill-defined as the estimated default probabilities are zero. Kijima and Komoribayashi [1998] propose a technique of risk premium …