Bond Market Structure in the Presence of Marked Point Processes

Björk, Tomas; Kabanov, Yuri; Runggaldier, Wolfgang J.

doi:10.1111/1467-9965.00031

Cited by 346 publications

(253 citation statements)

References 23 publications

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“…In the next section, we construct an instantaneous forward rate jump-diffusion model based on the framework of Björk, Kabanov, and Runggaldier (1997). Assuming that multiple market point processes are independent and follow the Poisson process, we incorporate the jump dynamics in the LIBOR stochastic process such that the instantaneous forward rate process of ( , ) df t T can be described as…”

Section: The Range Accrual Interest Rate Swap (Rairs) Contractmentioning

confidence: 99%

“…Based upon Björk, Kabanov and Runggaldier (1997), modified with i independent jump processes, we employ the Itô formula to derive the stochastic process value of the zero coupon bond as follows…”

Section: T U Du F T T Dt Df T U Du F T T Dt T U Dt Du T U Dw Du H T Xmentioning

confidence: 99%

“…Later, research increasingly focused on the interest rate jump-diffusion model. Shikarawa (1991) employs a pure jump model to price derivatives; Björk, Kabanov and Runggaldier (1997) extend the Heath, Jarrow and Morton (1992) "drift condition" to incorporate market point process to derive the instantaneous forward rate jump-diffusion model. The jump size in the market point process is assumed to be drawn from a continuous distribution with multiple jump processes, each of which is associated with a constant jump value scaled by time-deterministic jump volatility.…”

Section: Introductionmentioning

confidence: 99%

“…Such a model allows for solving for a no-arbitrage condition and a risk-neutral probability measurement. Finally, following the model of Björk, Kabanov and Runggaldier (1997), Chiarella and To (2003) propose an instantaneous forward rate jump-diffusion model.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks

Lin

Wang

Chen

et al. 2017

The North American Journal of Economics and Finance

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As an important economic index, interest rates are assumed to be constant in the Black and Scholes model (1973); however, they actually fluctuate due to economic factors. Using a constant interest rate to evaluate derivatives in a stochastic model will produce biased results.This research derives the LIBOR market model with jump risks, assuming that interest rates follow a continuous time path and tend to jump in response to sudden economic shocks. We then use the LIBOR model with jump risk to price a Range Accrual Interest Rate Swap (RAIRS). Given that the multiple jump processes are independent, we employ numerical analysis to further demonstrate the influence of jump size, jump volatility, and jump frequency on the pricing of RAIRS. Our results show a negative relation between jump size, jump frequency, and the swap rate of RAIRS, but a positive relation between jump volatility and the swap rate of RAIRS. When new information emerges, the resulting increase in jump size reduces the value of LIBOR, which in turn lowers the value of RAIRS. Similarly, the value of RAIRS declines when the jump frequency of LIBOR increases. This is because jump frequency is associated with higher uncertainty risk, and the market pays out a premium for bearing such risk. On the other hand, when jump volatility increases, both parties must agree to a higher swap rate because the floating rate payer is subsidized by the fixed rate payer for bearing risk.

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Section: The Range Accrual Interest Rate Swap (Rairs) Contractmentioning

confidence: 99%

Section: T U Du F T T Dt Df T U Du F T T Dt T U Dt Du T U Dw Du H T Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks

Lin

Wang

Chen

et al. 2017

The North American Journal of Economics and Finance

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show abstract

“…To be more general one would have to consider strategies involving a continuum of bonds. This can be done (see [4] or Mike Tehranchi's PhD thesis 2002) but is beyond the scope of this course. For convenience we require Q to be an EMM (and not merely an ELMM) because then we have…”

Section: Generalitiesmentioning

confidence: 99%

Interest Rates and Related Contracts

Filipović

2009

Term-Structure Models

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On the role of state variables in interest rates models

Geman

Lacoste

2000

Appl. Stochastic Models Bus. Ind.

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This paper discusses the introduction and the selection of a finite set of state variable in arbitrage‐free models of the term structure of interest rates. We choose a Gaussian setting which offers, as it is well known, tractable computations, hence results easier to understand and interpret. We study the mathematical conditions under which interest rates can be taken as state variables and address the key issues of time homogeneity of the model for a given set of state variables and the role of the current yield curve. Lastly, we provide explicit empirical estimations for four different swap markets (France, Italy, Japan, United Kingdom) and show that the state variables extracted through the use of a Kalman filter approach can be identified with linear combinations of interest rates. Copyright © 2000 John Wiley & Sons, Ltd.

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Bond Market Structure in the Presence of Marked Point Processes

Cited by 346 publications

References 23 publications

Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks

Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks

Interest Rates and Related Contracts

On the role of state variables in interest rates models

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