Pricing Of Convertible Bonds And Related Credit Risk Management Under Stochastic Interest Sate Model

As a bond with dual nature of both debt and equity,the pricing of convertible bonds has always attracted the attention of scholars from all over the world.In the earliest research on convertible bonds,partial differential equation(PDE)was used.An analytical solution to the pricing of convertible bonds is obtained.However,in the real market,the interest rate changes randomly,and then the random interest rate model is introduced.With the development of the term structure of random interest rate,the problem of the pricing of convertible bonds is more profound,most of which are continuous time model.In the price analysis of convertible bonds,in order to meet the real market demand.In this paper,in addition to the random interest rate,which is an uncertain factor,the random volatility is also considered.The pricing of convertible bonds adopts the three-branch tree model which is more advantageous for special bonds.Suppose there are three possibilities for the price change of the bond,namely,it goes up,it stays steady and it goes down.The idea of a fuzzy intuition set is used with respect to the three possible probabilities of change.In this paper,convertible bonds are regarded as financial derivatives composed of European call options and ordinary interest-paying claims.The pricing model of single-period convertible bond and multi-period convertible bond are discussed.After that,the risks faced by convertible bonds are discussed.Due to a series of uncertain factors in the market,Bonds are exposed to market risks and credit risks.Because convertible bonds are equity,if the stock price is ideal,Bondholders have the right to convert convertible bonds into stocks,which offsets the market risk of convertible bonds.If the issuer defaults,creditors are exposed to credit risk,In this paper,the repayment date of the company is allowed to be extended according to the different conditions of the rival company’s economy.Give a fair and reasonable judgment of the company’s default,and construct a credit risk transfer model under reasonable assumptions.By buying credit default swaps(CDS),the creditor transfers the credit risk faced by the holder of the debt to the seller of the default swap contract to avoid the risk faced by the holder.