An analytical approximation formula for the pricing of credit default swaps with regime switching

2021 ◽  
Vol 63 ◽  
pp. 143-162
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING

2021 ◽  
pp. 1-20
Author(s):  
XIN-JIANG HE ◽  
SHA LIN
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

Abstract We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments.

scholarly journals The Pricing and Hedging of an Attainable Claim in a Hybrid Black–Scholes Model under Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Kuanhou Tian ◽  
Yanfang Li ◽  
Guixin Hu
Keyword(s):  
Regime Switching ◽  
The Self ◽  
Black Scholes Model ◽  
Complete Market ◽  
Black Scholes ◽  
Theoretical Results

This article formulates and dissects a Black–Scholes model with regime switching that can be used to describe the performance of a complete market. An explicit integrand formula ϕ t , ω is obtained when the T -claim F ω is given for an attainable claim in this complete market. In addition, some perfect results are presented on how to hedge an attainable claim for this Black–Scholes model, and the price p of the European call and the self-financing portfolio θ t = θ 0 t , θ 1 t are given explicitly. Finally, some concluding remarks are provided to illustrate the theoretical results.

scholarly journals PRICING SOVEREIGN CONTINGENT CONVERTIBLE DEBT

2018 ◽  
Vol 21 (08) ◽  
pp. 1850049
Author(s):  
ANDREA CONSIGLIO ◽  
MICHELE TUMMINELLO ◽  
STAVROS A. ZENIOS
Keyword(s):  
Regime Switching ◽  
Sovereign Debt ◽  
Credit Default Swap ◽  
Convertible Bonds ◽  
Pricing Model ◽  
American Option Pricing ◽  
Market Index ◽  
Credit Default ◽  
Hidden Markov Process ◽  
Contingent Convertible Debt

We develop a pricing model for Sovereign Contingent Convertible bonds (S-CoCo) with payment standstills triggered by a sovereign’s Credit Default Swap (CDS) spread. We model CDS spread regime switching, which is prevalent during crises, as a hidden Markov process, coupled with a mean-reverting stochastic process of spread levels under fixed regimes, in order to obtain S-CoCo prices through simulation. The paper uses the pricing model in a Longstaff–Schwartz American option pricing framework to compute future state contingent S-CoCo prices for risk management. Dual trigger pricing is also discussed using the idiosyncratic CDS spread for the sovereign debt together with a broad market index. Numerical results are reported using S-CoCo designs for Greece, Italy and Germany with both the pricing and contingent pricing models.

scholarly journals Analytically Pricing Credit Default Swaps Under a Regime-Switching Model

2019 ◽  
Vol 18 (03) ◽  
pp. 1950021
Author(s):  
Wenting Chen ◽  
Xin-Jiang He ◽  
Xinzi Qiu
Keyword(s):  
Regime Switching ◽  
Numerical Experiments ◽  
Credit Default Swap ◽  
Credit Default Swaps ◽  
Default Probability ◽  
Regime Switching Model ◽  
Switching Model ◽  
Credit Default ◽  
Default Swap ◽  
Closed Form Formula

In this paper, we consider the valuation of a CDS (credit default swap) contract when the reference asset is assumed to follow a regime-switching model with the volatility allowed to jump among different states. Our motivation originates from empirical evidence demonstrating the existence of regime-switching in real markets. The default probability is analytically derived first, based on which a closed-form formula for the CDS price is obtained so that it can be easily implemented for practical purposes. Finally, numerical experiments are carried out to show quantitatively some properties of the CDS price under the regime-switching model.

scholarly journals Regime-Switching Determinants for Spreads of Emerging Markets Sovereign Credit Default Swaps

2018 ◽  
Vol 10 (8) ◽  
pp. 2730 ◽  
Author(s):  
Jason Ma ◽  
Xiang Deng ◽  
Kung-Cheng Ho ◽  
Sang-Bing Tsai
Keyword(s):  
Regime Switching ◽  
Dominant Role ◽  
Credit Default Swap ◽  
Switching Effect ◽  
Cross Sectional ◽  
Sovereign Credit ◽  
Flight To Quality ◽  
Good State ◽  
Credit Default ◽  
Country Specific

Using the Markov regime switching approach, we investigate the dependency of short term sovereign credit default swap (SCDS) spread changes on a nation’s country-specific fundamental factors, local, regional and macroeconomic global factors. We find that the significance of the determinants of SCDS spread changes differ across the two states of our regime-switching model. Specifically, in the good state, the weekly SCDS spread changes are mainly determined by local, regional and fundamental factors; whereas global variables have a stronger influence in the bad regime. In particular, US market returns play a dominant role in influencing the SCDS spread change in the bad state suggesting loss aversion and flight–to–quality behavior of investors. We then examine the cross-sectional differences of the above regime switching effect based on country-specific characters and find that the regime switching effect is associated with a nation’s country-specific characters such as openness, economic size and so forth.

scholarly journals Comparison of the Analytical Approximation Formula and Newton's Method for Solving a Class of Nonlinear Black–Scholes Parabolic Equations

2016 ◽  
Vol 16 (1) ◽  
pp. 35-50 ◽  
Author(s):  
Karol Ďuriš ◽  
Shih-Hau Tan ◽  
Choi-Hong Lai ◽  
Daniel Ševčovič
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Option Price ◽  
Nonlinear Effects ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Model Parameters ◽  
Diffusion Term ◽  
Feedback Effects ◽  
Black Scholes

AbstractMarket illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. In this paper, different linearization techniques such as Newton's method and the analytic asymptotic approximation formula are adopted and compared for a wide class of nonlinear Black–Scholes equations including, in particular, the market illiquidity model and the risk-adjusted pricing model. Accuracy and time complexity of both numerical methods are compared. Furthermore, market quotes data was used to calibrate model parameters.

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