Sensitivity Analysis of Catastrophe Bond Price Under the Hull–White Interest Rate Model

2016 ◽  
pp. 301-314
Author(s):  
Anatoliy Malyarenko ◽  
Jan Röman ◽  
Oskar Schyberg
Keyword(s):  
Sensitivity Analysis ◽  
Interest Rate ◽  
Rate Model ◽  
Bond Price ◽  
Interest Rate Model

Fractal Interest Rate Model without Ito Formula

2008 ◽  
Vol 16 (1) ◽  
pp. 21-48
Author(s):  
Joon Hee Rhee
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Asset Price ◽  
Rate Theory ◽  
Itô Formula ◽  
Rate Model ◽  
Bond Price ◽  
Ito Formula ◽  
Interest Rate Dynamics ◽  
Interest Rate Model

Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling. Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.

scholarly journals COHERENT CHAOS INTEREST-RATE MODELS

2015 ◽  
Vol 18 (03) ◽  
pp. 1550016
Author(s):  
DORJE C. BRODY ◽  
STALA HADJIPETRI
Keyword(s):  
Interest Rate ◽  
General Context ◽  
Rate Model ◽  
Bond Price ◽  
Linear Superposition ◽  
Pricing Kernel ◽  
Interest Rate Models ◽  
Multiple Copies ◽  
Rate Processes ◽  
Interest Rate Model

The Wiener chaos approach to interest-rate modeling arises from the observation that in the general context of an arbitrage-free model with a Brownian filtration, the pricing kernel admits a representation in terms of the conditional variance of a square-integrable generator, which in turn admits a chaos expansion. When the expansion coefficients of the random generator factorize into multiple copies of a single function, the resulting interest-rate model is called "coherent", whereas a generic interest-rate model is necessarily "incoherent". Coherent representations are of fundamental importance because an incoherent generator can always be expressed as a linear superposition of coherent elements. This property is exploited to derive general expressions for the pricing kernel and the associated bond price and short rate processes in the case of a generic nth order chaos model, for each n ∈ ℕ. Pricing formulae for bond options and swaptions are obtained in closed form for a number of examples. An explicit representation for the pricing kernel of a generic incoherent model is then obtained by use of the underlying coherent elements. Finally, finite-dimensional realizations of coherent chaos models are investigated and we show that a class of highly tractable models can be constructed having the characteristic feature that the discount bond price is given by a piecewise-flat (simple) process.

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.

scholarly journals DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

2020 ◽  
pp. 1-16
Author(s):  
Udeme O. Ini ◽  
Obinichi C. Mandah ◽  
Edikan E. Akpanibah
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Hjb Equation ◽  
Pension Scheme ◽  
Theoretic Approach ◽  
Rate Model ◽  
Risky Assets ◽  
Investment Plan ◽  
Interest Rate Model ◽  
The Impact

This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

scholarly journals Nonparametric estimation and specification testing of a two-factor interest rate model

2021 ◽  
Author(s):  
Brennan Scott Thompson
Keyword(s):  
Interest Rate ◽  
Nonparametric Estimation ◽  
Rate Model ◽  
Specification Testing ◽  
Interest Rate Model

Nonparametric estimation and specification testing of a two-factor interest rate model

scholarly journals Stock loan valuation under a stochastic interest rate model

2015 ◽  
Vol 70 (8) ◽  
pp. 1757-1771 ◽  
Author(s):  
Wenting Chen ◽  
Liangbin Xu ◽  
Song-Ping Zhu
Keyword(s):  
Interest Rate ◽  
Stochastic Interest Rate ◽  
Rate Model ◽  
Stochastic Interest ◽  
Interest Rate Model ◽  
Stock Loan
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