scholarly journals Multiscale Analysis on the Pricing of Intensity-Based Defaultable Bonds

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Sun-Hwa Cho ◽  
Jeong-Hoon Kim ◽  
Yong-Ki Ma
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Multiscale Analysis ◽  
Slow Time ◽  
Bond Price ◽  
Constant Intensity ◽  
Interest Rate Derivatives ◽  
Default Intensity ◽  
Defaultable Bonds ◽  
The Impact

This paper studies the pricing of intensity-based defaultable bonds where the volatility of default intensity is assumed to be random and driven by two different factors varying on fast and slow time scales. Corrections to the constant intensity of default are obtained and then how these corrections influence the term structure of interest rate derivatives is shown. The results indicate that the fast scale correction produces a more significant impact on the bond price than the slow scale correction and the impact tends to increase as time to maturity increases.

Pricing interest rate derivatives under stochastic volatility

2011 ◽  
Vol 37 (1) ◽  
pp. 72-91 ◽  
Author(s):  
Nabil Tahani ◽  
Xiaofei Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Alternative Methods ◽  
Future Research ◽  
Content Type ◽  
Interest Rate Derivatives ◽  
Affine Term Structure ◽  
Affine Term Structure Models ◽  
Term Structure Models

PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

REGIME SWITCHING TERM STRUCTURE MODEL UNDER PARTIAL INFORMATION

2011 ◽  
Vol 14 (02) ◽  
pp. 265-294 ◽  
Author(s):  
HIDENORI FUTAMI
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Regime Switching ◽  
Regime Shift ◽  
Partial Information ◽  
Market Price ◽  
Full Information ◽  
Bond Price ◽  
Term Structure Model ◽  
The Interest Rate

In this study, we attempt to calculate the term structure of the interest rate under partial information using a model in which the mean reversion level of the short rate changes in accordance with a regime shift in the economy. Under partial information, an investor observes the history of only the short rate and not a regime shift; hence, calculating the term structure of the interest rate is reduced to the problem of filtering the current regime from observable short rates. Therefore, we calculate it using the filtering theory that estimates a stochastic process from noisy observations, and investigate the effects of the regime shift under partial information on the market price of risk and the volatility of a bond price compared with those under full information, in which the regime is assumed to be observable. We find that, under partial information, the regime-shift risk converts into the diffusion risk. As a result, we find that both the market price of diffusion risk and the volatility of a bond price under partial information become stochastic, even though these under full information are constant.

A COMPLETE YIELD CURVE DESCRIPTION OF A MARKOV INTEREST RATE MODEL

2003 ◽  
Vol 06 (04) ◽  
pp. 317-326 ◽  
Author(s):  
ROBERT J. ELLIOTT ◽  
ROGEMAR S. MAMON
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Yield Curve ◽  
Forward Rate ◽  
Rate Model ◽  
Bond Price ◽  
Forward Measure ◽  
Expectation Hypothesis ◽  
Complete Set ◽  
Interest Rate Model

This paper aims to present a complete term structure characterisation of a Markov interest rate model. To attain this objective, we first give a proof that establishes the Unbiased Expectation Hypothesis (UEH) via the forward measure. The UEH result is then employed, which considerably facilitates the calculation of an explicit analytic expression for the forward rate f(t, T). The specification of the bond price P(t, T), yield rate Y(t, T) and f(t, T) gives a complete set of yield curve descriptions for an interest rate market where the short rate r is a function of a continuous time Markov chain.

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