scholarly journals Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Guoan Huang ◽  
Guohe Deng ◽  
Lihong Huang
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Factor Model ◽  
Integral Representations ◽  
Quadrature Formulas ◽  
Short Term ◽  
Put Option ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Coupon Bond

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided.

Pricing Longevity Bonds Under the Uncertainty Theory Framework

2019 ◽  
Vol 33 (06) ◽  
pp. 1959020
Author(s):  
Jianwei Gao ◽  
Huicheng Liu
Keyword(s):  
Interest Rate ◽  
Uncertainty Theory ◽  
Calculation Algorithm ◽  
Index Model ◽  
Survival Index ◽  
Vasicek Interest Rate Model ◽  
Longevity Bonds ◽  
Coupon Bond ◽  
Theory Framework ◽  
Pricing Formula

This paper aims to develop a new pricing approach for longevity bonds under the uncertainty theory framework. First, we describe the life expectancy by a canonical uncertain process and illustrate the dynamic of short interest rate via an uncertain Vasicek interest rate model. Then, based on these descriptions, we construct an uncertain survival index model and present its procedure for parameter estimation. By applying the chain rule, we derive a pricing formula of the uncertain zero-coupon bond. Considering that the financial market is incomplete, we put forward an uncertain distortion operator. Furthermore, based on the uncertain survival index, the uncertain zero-coupon bond pricing formula and the uncertain distortion operator, we develop a pricing formula of the uncertain longevity bond and its calculation algorithm. Finally, a numerical example is shown to illustrate the influence of parameters on the price of the uncertain longevity bond.

RENORMALIZATION OF BLACK-SCHOLES EQUATION FOR STOCHASTICALLY FLUCTUATING INTEREST RATE

2001 ◽  
Vol 04 (04) ◽  
pp. 621-634
Author(s):  
ALEXANDER G. MUSLIMOV ◽  
NIKOLAI A. SILANT'EV
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Numerical Solution ◽  
Short Term ◽  
Stochastic Component ◽  
Put Option ◽  
Stochastic Fluctuations ◽  
Black Scholes ◽  
The Interest Rate ◽  
American Put

We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

scholarly journals Bond portfolio's duration and investment term-structure management problem

2006 ◽  
Vol 2006 ◽  
pp. 1-19
Author(s):  
Daobai Liu
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Interest Rate Risk ◽  
Management Problem ◽  
Short Term ◽  
Bond Portfolio ◽  
Stochastic Interest ◽  
Bond Portfolios ◽  
Interest Rate Model ◽  
The Interest Rate

In the considered bond market, there are N zero-coupon bonds transacted continuously, which will mature at equally spaced dates. A duration of bond portfolios under stochastic interest rate model is introduced, which provides a measurement for the interest rate risk. Then we consider an optimal bond investment term-structure management problem using this duration as a performance index, and with the short-term interest rate process satisfying some stochastic differential equation. Under some technique conditions, an optimal bond portfolio process is obtained.

The Cox–Ingersoll–Ross Interest Rate Model

2019 ◽  
pp. 467-469
Author(s):  
Tomas Björk
Keyword(s):  
Interest Rate ◽  
Production Process ◽  
Factor Model ◽  
Square Root ◽  
Rate Model ◽  
Root Model ◽  
Interest Rate Model ◽  
Special Case ◽  
Square Root Model

In this chapter we study a special case of the factor model presented in Chapter 36. Assuming log utility and a square root model for the production process we derive the Cox–Ingersoll–Ross short rate model.

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