Hull-white model, Finance Basics

Hull-White model

As an extension of the Vasicek model, Hull-White model (1990) assumed that the short interest rate process follows the mean-reverting stochastic differential equation SDE:

drt = k(Θt - rt)dt +σdWt2,

where k and σ are positive constants,  Θt  is time-dependent function which will be used to currently fit the term structure of interest rate in the market.

while the interest rates are considerable to be stochastic, the tradeable asset evolves according to a geometric Brownian motion. So under the risk-natural measure Q, the dynamic of the instantaneous asset price is given by

dSt =rStdt + σSt dWt1,

where the two increments Wt1 and Wt2are independent Brownian motion process with

dWt1 dWt2 = ρ dt

 ρ representing the instantaneous correlation parameter between the asset price and the short interest rate.

Applying Ito lemma to (ekt) to find the differential of a time-dependent function of a stochastic interest rate process

D(r ekt) = ekt dr + k r ekt dt = kΘtekt dt + σekt dWt2

Then integrate both sides over [s,t] and simplify the equation,

1. Complete what I did before to prove  it is Gaussian and then  is following the normal distribution in clear and specific points?

Posted Date: 2/18/2013 1:20:43 AM | Location : United States







Related Discussions:- Hull-white model, Assignment Help, Ask Question on Hull-white model, Get Answer, Expert's Help, Hull-white model Discussions

Write discussion on Hull-white model
Your posts are moderated
Related Questions

Debt Finance Debt finance is a fixed return finance like the cost as interest is fixed on the par value as face value of debt. This is ideal to require if there's a strong equ

Constant payout ratio 1. This is whereas the firm will pay a fixed dividend rate as like 40 percent of earnings. The DPS would consequently fluctuate as the earnings per share

whom do you think rajendra should eat with and why

Discuss the applicability of an operating cycle in the vegetable growing business

Growth Rates Most Recent Fiscal Year Fiscal Year (-1) Fiscal Year (-2) Fiscal Year (-3) Annu


1. Suppose company A expects to increase unit sales of i-phone by 15% per year for the next 5 years. If you currently sell 3 million i-phones in one year, how many phones do you ex

Basic EOQ Model The basic inventory decision model is Economic Order Quantity or called EOQ model. This model is specified via the following equation as: Whereas:Q is

Advantages of Residual Theory 1. Saving on floatation costs No require to raise debt or equity capital as there is high retention of earnings that necessitates no floatat