A preference free partial differential equation for the term structure of interest rates

1996 ◽  
Vol 3 (3) ◽  
pp. 217-238 ◽  
Author(s):  
Carl Chiarella ◽  
Nadima El-Hassan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rates ◽  
Term Structure ◽  
Partial Differential

The Valuation of Carbon Bonds Linked with Carbon Price

2016 ◽  
Vol 16 (2) ◽  
pp. 345-359
Author(s):  
Shuhua Zhang ◽  
Zhuo Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rates ◽  
Carbon Price ◽  
Green Energy ◽  
Low Carbon ◽  
Partial Differential ◽  
Low Carbon Economy ◽  
Fuel Prices ◽  
Carbon Bonds

AbstractThe carbon bonds issued by countries or enterprises can solve the problem of funds in low carbon economy growth. Now most of carbon bonds pay fixed interest rates, and a few pay floating rates. The diversity of carbon bonds can attract more investors to participate green energy projects. The London Accord project group proposed the index linked carbon bonds in the World Band Government Borrowers' Forum in May 2009, and pointed out that the interest paid regularly may be linked to carbon price, governments' carbon emission targets, in-country fossil fuel prices or tariff feed-in prices. In this paper, the interests are considered to be linked with carbon prices in the condition of stochastic risk-free interest rate, and a partial differential equation is established for carbon bond interests. Also, a fitted finite volume method is employed to solve the resulting partial differential equation numerically, and on the basis of the valuation for zero-coupon bonds, the price of carbon bonds is obtained. Finally, some data are utilized for the calibration of the parameters in the established pricing models, and some numerical examples are presented and the effects of parameters on solutions are also demonstrated, which can provide references for the issuers of carbon bonds.

On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation

2020 ◽  
Vol 70 (4) ◽  
pp. 995-1002
Author(s):  
Beáta Stehlíková
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rates ◽  
Monetary Union ◽  
Financial Mathematics ◽  
Partial Differential ◽  
Stochastic Correlation ◽  
Wiener Processes ◽  
Random Shocks ◽  
Convergence Model

AbstractConvergence models of interest rates are used to model a situation, where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviour of the short rates can be correlated. In this paper we consider a stochastic correlation in a selected convergence model. A stochastic correlation has been already studied in different contexts in financial mathematics, therefore we distinguish differences which come from modelling interest rates by a convergence model. We provide meaningful properties which a correlation model should satisfy and afterwards we study the problem of solving the partial differential equation for the bond prices. We find its solution in a separable form, where the term coming from the stochastic correlation is given in its series expansion for a high value of the correlation.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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