机制转换模型中可违约权益的对冲（英文）
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摘要
给出了马氏链的表示定理,并且在马氏机制转换模型下考虑了可违约权益的对冲问题,利用马氏链的表示定理得到了可违约权益的动态对冲策略。
This paper presented a martingale representation for Markov chain, and investigated the hedging of defaultable claims in a Markov regime switching model. It derives the pricing dynamics of a defaultable claim and the self-financing trading strategy based on the savings account and defaultable bonds.
This paper presented a martingale representation for Markov chain, and investigated the hedging of defaultable claims in a Markov regime switching model. It derives the pricing dynamics of a defaultable claim and the self-financing trading strategy based on the savings account and defaultable bonds.
引文
[1]BIELECKI T R,JEANBLANC M,RUTKOWSKI M.Pricing and trading credit default swaps in a hazard process model[J].The Annals of Applied Probability 2008,18(6):2495-2529.
[2]BIELECKI T R,JEANBLANC M,RUTKOWSKI M.Paris-Princeton Lectures on Mathematical Finance 2003[M].Berlin:Springer,2004:1-132.
[3]BLANCHET-SCALLIET C,JEANBLANC M.Hazard rate for credit risk and hedging defaultable contingent claims[J].Finance and Stochastics,2004,8:145-159.
[4]BLANCHET-SCALLIET C,EYRAUD-LOISEL A,ROYER-CARENZI M.Hedging of defaultable contingent claims using BSDE with uncertain time horizon[J].Bulletin Francais d'Actuariat,2010,10(20):102-139.
[5]BIELECKI T R,JEANBLANC M,RUTKOWSKI M.Hedging of a credit default swaption in the CIR default intensity model[J].Finance and Stochastics,2011,15(3):541-572.
[6]FUJII M,TAKAHASHI A.Making mean-variance hedging implementable in a partially observable market[J].Quantitative Finance,2014,14(10):1709-1724.
[7]LAURENT J P,COUSIN A,FERMANIAN J D.Hedging default risks of CDOs in Markovian contagion models[J].Quantitative Finance,2011,11(12):1773-1791.
[8]ELLIOTT R J,CHAN L,SIU T K.Option pricing and esscher transform under regime switching[J].Annals of Finance,2005,1:423-432.
[9]LIANG X,WANG G J,DONG Y H.A Markov regime switching jump-diffusion model for the pricing of portfolio credit derivatives[J].Statistics and Probability Letters,2013,83:373-381.
[10]SIU T K.Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic ows[J].Applied Mathematics and Computation,2010,216:3184-3190.
[11]CAPPONI A,FIGUEROA-L譫PEZ J E.Dynamic portfolio optimization with a defaultable security and regime-switching[J].Mathematical Finance,2014,24(2):207-249.
[12]PROTTER P E.Stochastic Integration and Differential Equations[M].Berlin:Springer-Verlag,2004.
[13]BIELECKI T R,RUTKOWSKI M.Credit Risk:Modeling,Valuation and Hedging[M].Berlin:Springer-Verlag,2002.
[14]LANDO D.On Cox processes and credit risky securities[J].Review of Derivatives Research,1998,2:99-120.
[2]BIELECKI T R,JEANBLANC M,RUTKOWSKI M.Paris-Princeton Lectures on Mathematical Finance 2003[M].Berlin:Springer,2004:1-132.
[3]BLANCHET-SCALLIET C,JEANBLANC M.Hazard rate for credit risk and hedging defaultable contingent claims[J].Finance and Stochastics,2004,8:145-159.
[4]BLANCHET-SCALLIET C,EYRAUD-LOISEL A,ROYER-CARENZI M.Hedging of defaultable contingent claims using BSDE with uncertain time horizon[J].Bulletin Francais d'Actuariat,2010,10(20):102-139.
[5]BIELECKI T R,JEANBLANC M,RUTKOWSKI M.Hedging of a credit default swaption in the CIR default intensity model[J].Finance and Stochastics,2011,15(3):541-572.
[6]FUJII M,TAKAHASHI A.Making mean-variance hedging implementable in a partially observable market[J].Quantitative Finance,2014,14(10):1709-1724.
[7]LAURENT J P,COUSIN A,FERMANIAN J D.Hedging default risks of CDOs in Markovian contagion models[J].Quantitative Finance,2011,11(12):1773-1791.
[8]ELLIOTT R J,CHAN L,SIU T K.Option pricing and esscher transform under regime switching[J].Annals of Finance,2005,1:423-432.
[9]LIANG X,WANG G J,DONG Y H.A Markov regime switching jump-diffusion model for the pricing of portfolio credit derivatives[J].Statistics and Probability Letters,2013,83:373-381.
[10]SIU T K.Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic ows[J].Applied Mathematics and Computation,2010,216:3184-3190.
[11]CAPPONI A,FIGUEROA-L譫PEZ J E.Dynamic portfolio optimization with a defaultable security and regime-switching[J].Mathematical Finance,2014,24(2):207-249.
[12]PROTTER P E.Stochastic Integration and Differential Equations[M].Berlin:Springer-Verlag,2004.
[13]BIELECKI T R,RUTKOWSKI M.Credit Risk:Modeling,Valuation and Hedging[M].Berlin:Springer-Verlag,2002.
[14]LANDO D.On Cox processes and credit risky securities[J].Review of Derivatives Research,1998,2:99-120.