Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation

Heath, David; Jarrow, Robert A.; Morton, Anthony

doi:10.1142/9789812819222_0013

Cited by 172 publications

(217 citation statements)

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“…In these models, all discount bonds are priced relative to the stochastic short rate such that there are no arbitrage opportunities in their trading. Researchers have since developed such long-term interest rate models as the instantaneous forward rate model (Heath, Jarrow and Morton, 1992) and the LIBOR market model (Brace, Gatarak and Musiela, 1997), all based on the no-arbitrage condition. Merton (1976) points out that since stock price dynamics do not follow a continuous sample path, they should be modeled as a "jump" process with a non-continuous sample path that reflects the impact of the emergence of important new information.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

“…There has been some effort in the years after the publication of HJM [9] in 1992 to develop arbitrage-free models of other than instantaneous, continuously compounded rates. The breakthrough came 1997 with the publications of Brace-GatarekMusiela [5] (BGM), who succeeded to find a HJM type model inducing lognormal LIBOR rates, and Jamshidian [?…”

Section: Chapter 12 Market Modelsmentioning

confidence: 99%

Interest Rates and Related Contracts

Filipović

2009

Term-Structure Models

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“…The most popular approaches are equilibrium and no-arbitrage models. The no-arbitrage models follow the BlackScholes framework and ensure correct pricing of derivatives; the main contributions for no-arbitrage models are Hull and White (1990) and Heath et al (1992). The equilibrium framework provides exact fits to the observed term structure (Longstaff and Schwartz, 1992).…”

Section: Introductionmentioning

confidence: 99%

Yield curve modeling and forecasting using semiparametric factor dynamics

Härdle

Majer

2014

The European Journal of Finance

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Using a Dynamic Semiparametric Factor Model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method -dynamic Nelson-Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short term forecasting.JEL classification: G12, G17, C5, C4

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Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation

Cited by 172 publications

References 0 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

Yield curve modeling and forecasting using semiparametric factor dynamics

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