scholarly journals Structural Credit Risk Model with Jumps Based on Uncertainty Theory

2021 ◽  
Author(s):  
Hong Huang ◽  
Yufu Ning
Keyword(s):  
Differential Equation ◽  
Credit Risk ◽  
Behavioral Finance ◽  
Uncertainty Theory ◽  
Risk Model ◽  
Credit Default Swap ◽  
Uncertain Differential Equation ◽  
Underlying Asset ◽  
Stock Value ◽  
Proposed Model

Abstract Traditional finance studies of credit risk structured models are based on the assumption that the price of the underlying asset obeys a stochastic differential equation. However, according to behavioral finance, the price of the underlying asset is not entirely stochastic, and the credibility of financial investors also plays a very important role in asset prices. In this paper we introduce uncertainty theory to describe these credibility of investors and propose a new credit risk structured model with jumps based on the assumption that the underlying asset is described by an uncertain differential equation with jumps. The company default belief degree formula, zero coupon bond value and stock value formula are formulated. Company bond credit spread and credit default swap (CDS) pricing are studied as applications of the proposed model in uncertain markets.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

scholarly journals The impact of changes in the base and precious metals prices on credit risk factors

2020 ◽  
Vol 17 (2) ◽  
pp. 45-64
Author(s):  
Vladimir Živanović
Keyword(s):  
Risk Factors ◽  
Credit Risk ◽  
Risk Model ◽  
Precious Metals ◽  
Multivariate Regression Analysis ◽  
Metal Exchange ◽  
Analysis Model ◽  
Proposed Model ◽  
Credit Risk Model ◽  
The Impact

The changes in the prices of base and precious metals on the global metal market have a significant impact on credit risk factors. The link between these factors has been neglected over the years by traditional credit risk models. The inclusion of correlation coefficients within the set credit risk model will show the impact of these changes on other variables of credit risk over the years under review and the impact of these changes on the probability of default and the recovery rate. Changes in base metals prices on the London Metal Exchange (LME) for lead and zinc and the London Bullion Metal Association (LBMA) for gold and silver as precious metals were used in the proposed credit risk model for the period of ten years. The research was done by using the multivariate regression analysis model and based on the statistical model evaluation,the significant impact of all observed independent variables on the dependent variable of the proposed model was proved. The construction of the proposed model with proven predictability gives a scientific significance to the research that includes variables of models from different markets, which have a significant impact on the variables from the financial market.

Regime Dependent Determinants of Credit Default Swap Spread

2012 ◽  
Vol 20 (1) ◽  
pp. 41-64
Author(s):  
Hong-Bae Kim ◽  
Yeonjeong Lee ◽  
Sang Hoon Kang ◽  
Seong-Min Yoon
Keyword(s):  
Credit Risk ◽  
Interest Rates ◽  
Stock Returns ◽  
Risk Model ◽  
Credit Default Swap ◽  
Markov Switching Model ◽  
Stock Market Returns ◽  
Interest Level ◽  
Efficient Hedging ◽  
Credit Default Swap Spread

This study investigates the influence of theoretical determinants on the Korea sovereign CDS spreads from January 2007 to September 2009 based on structural credit risk model. For the analysis of determinants on the sovereign CDS spread, this study adopts interest swap rate as reference interest rate, and decomposes yields curve into two components, ie, interest level and slope. Considering multivariate regression in level and difference variables, Stock returns and Interest rates have a significant effect on the CDS spreads among the theoretical determinants of structural credit risk models. CDS spreads may behave quite differently during volatile regime compared with their behavior in tranquil regime. We therefore apply Markov switching model to investigate the possibility that the influence of theoretical determinants of CDS spread has a regime dependent behavior. In all regimes Korean sovereign CDS spreads are highly sensitive to stock market returns, whereas in tranquil regime interest rates also have influence on CDS spreads. We conclude that for the efficient hedging of CDS exposure trader should adjust equity hedge ratio to the relevant regime.

The pth moment exponential stability of uncertain differential equation with jumps

2020 ◽  
Vol 39 (3) ◽  
pp. 4419-4425
Author(s):  
Shiqin Liu ◽  
Liying Liu ◽  
Na Wang ◽  
Jianguang Zhang
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Uncertainty Theory ◽  
Axiom System ◽  
Uncertain Differential Equation ◽  
Necessary And Sufficient Condition ◽  
Pth Moment Exponential Stability ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Moment Exponential Stability

Under the axiom system of uncertainty theory, the paper mainly introduce the new definition of the pth moment exponential stability for uncertain differential equation with jumps. For illustrating the concept, some examples and counterexamples are given. Furthermore, we obtain a necessary and sufficient condition of stability in pth moment exponential for the linear uncertain differential equation with jumps. Also, the conclusion condition is illustrated very clearly by two examples.

SALAM CONTRACT WITH CREDIT RISK MODEL BY PARTIAL DIFFERENTIAL EQUATION APPROACH

2016 ◽  
Vol 78 (11) ◽  
Author(s):  
Azie Farhani Badrol Hisham ◽  
Maheran Mohd Jaffar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Risk Management ◽  
Credit Risk ◽  
Risk Model ◽  
Global Financial Crisis ◽  
Partial Differential ◽  
Major Subject ◽  
Contract Implementation ◽  
Credit Risk Model

In the acute phase of global financial crisis, the risk management issue has become a major subject that attracts the interest of many financial institutions. Risk management in Islamic finance is proven to be more challenging than the conventional due to shariah principals and regulations. Therefore, there is a need for an alternative Islamic derivative product that can compete with the existing conventional derivatives. This study proposes a traditional Islamic contract, which is salam, that can be built as a new Islamic derivative product. Since there is lack of quantitative study regarding salam contract implementation, this study introduces a mathematical model of commodity salam contract by considering credit risk element. The structural approach is the best credit risk model to describe the structure and properties of salam contract. However, because of the unique structure and boundary condition of salam contract, some adjustments need to be considered. In deriving the partial differential equation that describes the dynamic behaviour of commodity salam contract with credit risk, the risk neutral valuation was employed.

Uncertain Statistics and COVID-19 Spread in China

2021 ◽  
pp. 2150008
Author(s):  
Waichon Lio
Keyword(s):  
Differential Equation ◽  
Regression Analysis ◽  
Uncertainty Theory ◽  
Hypothesis Test ◽  
Uncertain Differential Equation ◽  
Uncertainty Distribution ◽  
Times Series ◽  
Mathematical Techniques ◽  
Uncertain Statistics ◽  
Estimation Of Uncertainty

Uncertain statistics is a set of mathematical techniques for collecting, analyzing and interpreting data by uncertainty theory. In this paper, the main topics of uncertain statistics, including estimation of uncertainty distribution, uncertain regression analysis, uncertain times series, uncertain differential equation and uncertain hypothesis test, are reviewed. Furthermore, by the application to the COVID-19 spread in China, the advantages of those techniques in uncertain statistics are sorted out.

PRICING-HEDGING DUALITY FOR CREDIT DEFAULT SWAPS AND THE NEGATIVE BASIS ARBITRAGE

2019 ◽  
Vol 22 (06) ◽  
pp. 1950032
Author(s):  
JAN-FREDERIK MAI
Keyword(s):  
Credit Risk ◽  
Risk Model ◽  
Credit Default Swap ◽  
Interest Rate Risk ◽  
Market Prices ◽  
Risk Hedging ◽  
Credit Default ◽  
Hedging Problem ◽  
Risk Free Rate ◽  
Free Rate

Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swap (CDS) contracts. This static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with observed CDSs. This duality is maintained when the risk-free rate is shifted parallel. In practice, there is a unique parallel shift [Formula: see text] that is consistent with observed market prices for bond and CDSs. The resulting, risk-free trading strategy in case of positive [Formula: see text] earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and [Formula: see text] defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, [Formula: see text] is a premium for taking the residual risks of a bond investment after interest rate risk and credit risk are hedged away. Chiefly, these are liquidity and legal risks.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

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