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.

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.

scholarly journals A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 5
Author(s):  
Mao Chen ◽  
Guanqi Liu ◽  
Yuwen Wang
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Hybrid Model ◽  
Approximate Formula ◽  
Closed Form Solution ◽  
Sampling Frequency ◽  
Form Solution ◽  
Variance Swaps ◽  
Return Variance ◽  
Pricing Formula

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results ; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and Ito^’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable.

Asset pricing under general collateralization

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750019
Author(s):  
Yanhui Mi
Keyword(s):  
Asset Pricing ◽  
Market Model ◽  
Model Framework ◽  
Libor Market Model ◽  
Sabr Model ◽  
Bond Option ◽  
Coupon Bond ◽  
Joint Evolution ◽  
Pricing Formula

We consider the valuation of collateralized derivative contracts such as bond option or Caplet contracts. We allow for posting different collaterals such as securities or cash for the derivatives and its hedges. The pricing is based on modeling the joint evolution of collateral rate and the spread between collaterals. The Hull–White models are applied to collateral rate and spread to generate the closed pricing formula for zero coupon bond option. We also derive the pricing formula for Caplet under the Libor Market model and SABR model framework.

Sensitivities under G2++ model of the yield curve

2017 ◽  
Vol 04 (01) ◽  
pp. 1750008
Author(s):  
H. Jaffal ◽  
Y. Rakotondratsimba ◽  
A. Yassine
Keyword(s):  
Interest Rate ◽  
Yield Curve ◽  
Gaussian Model ◽  
Interest Rate Derivatives ◽  
Market Participants ◽  
Liability Management ◽  
Analytic Expressions ◽  
Text Model ◽  
The Interest Rate ◽  
Coupon Bond

The two-additive-factor Gaussian model G2[Formula: see text] is a famous stochastic model for the instantaneous short rate. It has functional qualities required in various practical purposes, as in Asset Liability Management and in Trading of interest rate derivatives. Though closed formulas for the prices of various main interest-rate instruments are known and used under the G2[Formula: see text] model, it seems that references for the corresponding sensitivities are not clearly presented over the financial literature. To fill this gap is one of our purposes in the present work. We derive here analytic expressions for the sensitivities of zero-coupon bond, coupon-bearing bonds, portfolio of coupon bearing bonds. The sensitivities under consideration here are those with respect to the shocks linked to the unobservable two-uncertainty shock risk/opportunity factors underlying the G2[Formula: see text] model. As a such, the hedging of a position sensitive to the interest rate by means of a portfolio (in accordance with the market participants practice) becomes easily transparent as just resulting from the balance between the various involved sensitivities.

scholarly journals Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chubing Zhang ◽  
Ximing Rong
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Plan Member ◽  
Cara Utility ◽  
Hamilton Jacobi Bellman ◽  
Coupon Bond

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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