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
Explain the term- Order Brokers receive numerous different types of buying and selling orders from their customers. Brokerage orders very as to the price at which order may

Profit maximization - Objectives of Business Entity Conventionally, this was considered to be the main goal of the firm. Profit maximization refers to getting the highest poss

Constraints of Venture Capital in US 1. Require of rich investors in US, thus inadequate equity capital. 2. Inefficiencies of stock market - NSE is investors and inefficien

From the following cost, production and sales data of Decors Motor Ltd., prepare comparative income statement for three years under (i) absorption costing method, and (ii) marginal

Cash Cycle and Cash Turnovers Cash Cycle refers to the amount of time which elapses from the point whenever the firms create a cash outlay to purchase raw materials to the poi

1. Describe the similarities and differences in between an ordinary annuity, an annuity due, and perpetuity.  Provide a methodical answer, including examples to demonstrate your po

Definition of 'Capital Budgeting': The process in which a business calculates whether projects such as building a new plant or investing in a long-term risk are worth pursuing

Calculate total number of ordinary shares Example Company XYZ Ltd has sold 10,000 ordinary shares of Shs.30 as partly called up plus 20,000 Shs.45 preference shares, tha

Market Model - Methods of Computing Cost of Capital This model is utilized to establish the percentage cost of ordinary share capital cost of equity (K e ). If an investor is

Stone Container is a major producer of cardboard boxes. Stone Container has $10M in outstanding equity. In addition, it has $2M in outstanding debt. The debt is a ten-yearmortgage