AN EXTENSION OF THE BRODY–HUGHSTON–MACRINA APPROACH TO MODELING OF DEFAULTABLE BONDS

The innovative information-based framework for credit risk modeling, proposed recently by Brody, Hughston, and Macrina, is extended to a more general and practically important setup of random interest rates. We first introduce the market model, and we derive an explicit expression for defaultable bond price. Next, the dynamics of the information process and dynamics of defaultable bond are found for both deterministic and random interest rates. Finally, the valuation and hedging of derivative securities are briefly examined. In particular, the valuation formula for a European option on a defaultable bond is established.

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Interactions between Market and Credit Risk: Modeling the Joint Dynamics of Default-free and Defaultable Bond Term Structures

SSRN Electronic Journal ◽

10.2139/ssrn.354480 ◽

2002 ◽

Cited By ~ 6

Author(s):

Roger Walder

Keyword(s):

Credit Risk ◽

Risk Modeling ◽

Defaultable Bond ◽

Term Structures ◽

Joint Dynamics ◽

Credit Risk Modeling

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INTERBANK CREDIT RISK MODELING WITH SELF-EXCITING JUMP PROCESSES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500399 ◽

2020 ◽

Vol 23 (06) ◽

pp. 2050039

Author(s):

CHARLES GUY NJIKE LEUNGA ◽

DONATIEN HAINAUT

Keyword(s):

Credit Risk ◽

Interest Rates ◽

Arrival Rate ◽

Jump Processes ◽

Reduced Form ◽

Rate Theory ◽

Risk Modeling ◽

Interbank Market ◽

The Impact ◽

Swap Rates

The credit crunch of 2007 caused major changes in the market of interbank rates making the existing interest rate theory inconsistent. This paper puts forward one way to reconcile practice and theory by modifying the arbitrage-free condition. In this framework, the forward Libor rate is no longer considered as a risk-free rate and the credit and liquidity risks within the interbank market partly drive its dynamics. In a similar manner to the multiple-curve approach, we model the evolution of default-free rates, assimilated to overnight interest swap rates, and the default times of an interbank market segment determined by its tenor. For each segment, we use the reduced form approach to model the arrival rate of defaults with a self-exciting jump-diffusion process. Then, we deduce the dynamics of the spot forward Libor rates and provide closed-form approximation pricing formulae for options on forward Libor rates and swap rates. Even in a context of negative interest rates and compared to other forms of intensity processes such as a CIR, the self-excitation property allows a better understanding of the spread OIS-IRS and provides information about the interbank credit risk. Furthermore, our framework enables to parse the impact of the interbank credit risk on forward Libor as well as on interest rates derivatives like caps, floors, and swaptions.

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Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Mathematics ◽

10.3390/math8112033 ◽

2020 ◽

Vol 8 (11) ◽

pp. 2033

Author(s):

Zhehao Huang ◽

Zhenghui Li ◽

Zhenzhen Wang

Keyword(s):

Credit Risk ◽

Default Risk ◽

Credit Rating ◽

Joint Effect ◽

Corporate Bond ◽

Subprime Crisis ◽

Risk Modeling ◽

Bond Price ◽

Closed Form Solutions ◽

Financial Index

Credit risk modeling by debt pricing has been a popular theme in both academia and practice since the subprime crisis. In this paper, we devote our study to the indifferent price of a corporate bond with credit risk involving both default risk and credit rating migration risk in an incomplete market. The firm’s stock and a financial index on the market as tradable assets are introduced to hedge the credit risk, and the bond price is determined by the indifference of investors’ utilities with and without holding the bond. The models are established under the structural framework and result in Hamilton–Jacobi–Bellman (HJB) systems regarding utilities subject to default boundary and multiple migration boundaries. According to dynamic programming theory, closed-form solutions for pricing formulas are derived by implementing an inverted iteration program to overcome the joint effect of default and multiple credit rating migration. Therefore, with the derived explicit pricing formulas for the corporate bond, the models can be easily applied in practice, and investors can generate their strategies of hedging the credit risk by easily analyzing the impacts of the parameters on the bond price.

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SYMMETRIES IN JUMP-DIFFUSION MODELS WITH APPLICATIONS IN OPTION PRICING AND CREDIT RISK

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024903001803 ◽

2003 ◽

Vol 06 (02) ◽

pp. 135-172 ◽

Cited By ~ 4

Author(s):

J. K. HOOGLAND ◽

C. D. D. NEUMANN ◽

M. H. VELLEKOOP

Keyword(s):

Credit Risk ◽

Credit Default Swap ◽

Jump Diffusion ◽

Diffusion Models ◽

Market Model ◽

Derivative Securities ◽

Default Correlation ◽

Wiener Processes ◽

Basket Option ◽

Credit Default

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of "change of numeraire", but in recent work it was shown that when invoked as a fundamental first principle, it provides a powerful alternative method for the derivation of prices and hedges of derivative securities, when prices of the underlying tradables are driven by Wiener processes. In this article we extend this work to the pricing problem in markets driven not only by Wiener processes but also by Poisson processes, i.e. jump-diffusion models. It is shown that in this case too, the focus on symmetry aspects of the problem leads to important simplifications of, and a deeper insight into the problem. Among the applications of the theory we consider the pricing of stock options in the presence of jumps, and Lévy-processes. Next we show how the same theory, by restricting the number of jumps, can be used to model credit risk, leading to a "market model" of credit risk. Both the traditional Duffie-Singleton and Jarrow-Turnbull models can be described within this framework, but also more general models, which incorporate default correlation in a consistent way. As an application of this theory we look at the pricing of a credit default swap (CDS) and a first-to-default basket option.

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Strategi Pengelolaan Risiko dan Peningkatan Kualitas Pengelolaan Kas Negara

Indonesian Treasury Review Jurnal Perbendaharaan Keuangan Negara dan Kebijakan Publik ◽

10.33105/itrev.v2i2.26 ◽

2017 ◽

Vol 2 (2) ◽

pp. 43-54

Author(s):

Agung Mulyono

Keyword(s):

Interest Rates ◽

Financial Risk ◽

Vector Autoregression ◽

Secondary Market ◽

Key Factors ◽

Bond Price ◽

Hedging Strategy ◽

Foreign Loan ◽

Term Operation ◽

Loan Interest Rates

Cash management is one of treasury’s main functions in which has a potential financial risk. A potential financial risk emerges when State Treasurer manages cash surplus and or/ shortages in order to maintain optimum liquidity. By applying Vector Autoregression (VAR) system on empirical data provided by Bank Indonesia and the Ministry of Finance of Indonesia, we found that currency value flunctuation is a significant factor for repayment value of foreign loan. Interest rates and amount of government’s bond held by foreign investors are also variables impacted on government’s bond price movement in secondary market. Currency value flunctuation and price of government’s bond in secondary market are the key factors that have to be considered by State Treasurer (BUN) in managing state’s money. Hedging strategy by using derivatif product is possible to be utilized by State Treasurer (BUN) due to it’s flexibility for short-term operation. Abstrak Pengelolaan kas negara merupakan salah satu fungsi pokok perbendaharaan yang dalam proses pelaksanaannya menyimpan potensi berbagai risiko keuangan. Risiko keuangan, khususnya dalam investasi berpotensi muncul ketika Bendahara Umum Negara (BUN) melakukan kegiatan pengelolaan kelebihan dan/ kekurangan kas dalam rangka menjamin ketersediaan dan optimalisasi kas. Dengan menggunakan analisis Vector Autoregression (VAR) atas data empiris yang diperoleh dari Bank Indonesia dan Kementerian Keuangan Indonesia, penulis menemukan bahwa fluktuasi nilai tukar mata uang merupakan faktor yang signifikan terhadap besaran pembayaran utang luar negeri pemerintah. Tingkat suku bunga acuan dan pergerakan besaran kepemilikan SUN oleh investor asing juga merupakan variabel yang berpengaruh terhadap pergerakan harga SUN di pasar sekunder. Fluktuasi nilai tukar mata uang dan pergerakan harga SUN di pasar sekunder menjadi faktor penting dalam pelaksanaan investasi yang dilakukan BUN dalam rangka pengelolaan kelebihan dan/ kekurangan kas. Berdasarkan hasil tersebut, strategi pengelolaan risiko atau hedging dengan menggunakan produk-produk derivatif dalam pengelolaan kelebihan dan/ kekurangan kas jangka pendek – menengah sangat dimungkinkan karena sifat instrumen derivatif yang fleksibel.

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