Research On Markov Chain Pricing Model Of Hybrid Triggered CoCo Bonds

The subprime crisis in 2008 exposed the vulnerability of the banking system.Basel Ⅲ further strengthened the supervision of bank capital and encouraged banks to establish emergency capital mechanism.CoCo bonds are bonds that can automatically convert to equity or be written down in predetermined proportions under certain trigger events,including accounting,market and regulatory triggers.CoCo bond is the core of contingency capital mechanism,and also an important form of contingent capital.With the continuous expansion of CoCo bond market,the pricing of CoCo bond has gradually become one of the hot topics in theoretical research.The research of this paper is mainly based on the mixed trigger CoCo bonds issued by Credit Suisse in the second public issue.The trigger event of this bond is composed of accounting trigger and regulatory trigger.After the trigger,the CoCo bonds will be converted into a fixed number of stocks,and the conversion price is the stock price observed at the trigger moment.Based on the reductive model,this paper describes the accounting trigger and regulatory trigger into the process of stock value by using default explicit function,analyzes the cash flow process of CoCo bonds with mixed trigger,and obtains the value before the trigger of CoCo bonds.Using stock price as valuation unit,the equity value of CoCo bonds under the new probability measure is obtained by measure transformation.In the framework of Markov chain,the transition density matrix of CoCo bonds is obtained by Markov Copula condition,and the relationship between the transition density matrix of Markov chain under the new measure and the transition density matrix under the original measure is proved.The survival probability and joint condition generation probability of CoCo bonds under the trigger conditions under each probability measure are obtained respectively.Using the domain flow decomposition theorem and Feynman-Kac formula,the corresponding partial differential pricing equation is derived.The stochastic process problem of CoCo bond pricing is transformed into the solution problem of partial differential equation,and the implicit difference method is used to carry out numerical analysis of the derived partial differential equation.The relationship between the value of mixed trigger CoCo bond and stock price and the sensitivity of the value of mixed trigger CoCo bond to different parameter values are discussed.Based on the reductive model,this paper puts forward a new idea on the research of CoCo bond pricing model and method by using measure transformation and Markov chain method.