Hull-white model, Finance Basics

Assignment Help:

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?


Related Discussions:- Hull-white model

Financial analysis, Financial analysis: Financial analysis (also defin...

Financial analysis: Financial analysis (also defined to as financial statement analysis or accounting analysis or Analysis of finance) defines to an assessment of the viabilit

Return on the annuity, An insurance company offers you and end of year annu...

An insurance company offers you and end of year annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9%. What is the most you would be willin

Determaine the dol and business risk, From the following selected operating...

From the following selected operating date, determaine the DOL. Which company has the greater amount of business risk? Why? Particulars A Ltd

Example of baumol's model, Example of Baumol's Model ABC Ltd. creates ...

Example of Baumol's Model ABC Ltd. creates cash payments of Shs.10, 000 per week.  The interest rate at marketable securities is 12 percent and every moment the company sells

Financial management, Financial Management On the other hand a financi...

Financial Management On the other hand a financial manager has to meet the company's strategic or long term needs as long term investment are helpful to the company since:

Determine the component of return, Determine the Component of Return ...

Determine the Component of Return Rate of return from an investment consists of the two: (i) Yield: Interest or dividend received is called yield. (ii) Capital Appreci

APR, Determine how much of a total loan payment applies towards principal a...

Determine how much of a total loan payment applies towards principal and how much applies towards interest for a home mortgage of $177,219 with a fixed APR of 7.5% of 20 years

Inventory management - supply chain management, Inventory Management - Supp...

Inventory Management - Supply Chain Management Determination of the best ordering policy in a manufacturing organisation In a manufacturing organisation, procurement may ha

Tests of term structure of interest rates theories, Tests of Term Structure...

Tests of Term Structure of Interest Rates Theories Various tests have been conducted mainly in USA and they show that all the three (3) theories have some validity and therefo

#title.ASF, Ask questioAustralian’s Speleological App Projectn #Minimum 100...

Ask questioAustralian’s Speleological App Projectn #Minimum 100 words accepted#

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd