Consider the HullWhite model where the short rate process follows where Z t is a Brownian process under the risk neutral measure Q Using the relation show that Accordingly, the mean and variance of t T r(u) du are found to be Compute the bond price B(r, t T) dr (t) art dt o dZt, ...

The Answer is in the image, click to view ...

Consider the HullWhite model where the short rate process follows where Z t is a Brownian process

Question:

Consider the Hull–White model where the short rate process follows

dr = [(t) art] dt + o dZt, -

where Z_t is a Brownian process under the risk neutral measure Q. Using the relation

d[r(t)eat] = $(t)eat dt + oeat dz(t), show that

S.T 1- e-(T-t) r(u) du = r(t). n J_J+ 1 = r(t). JJ - e-(T-1) + oe-a(u-s) dz(s) du (u)e-a(u-s) ds du T [ (u).

Accordingly, the mean and variance of ∫_t^T r(u) du are found to be

1 (1) - e-a(T-1) T T var (f

Compute the bond price B(r, t; T).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

See More Books

Question Posted: Dec 05, 2023 12:56 AM

See More Questions

Consider the SDE for the spot rate rt (a) Show that 9Suppose we brought in another equation containing B(t, U): (b) What do these two equations imply for the conditional mean and variance of spot...
The dynamics of the instantaneous forward rate F(t,T ) under the risk neutral measure Q is governed by where (Z 1 (t)Z m (t)) T is an m-dimensional Brownian process under Q. Let (W 1 (t) W m (t)) T...
Show that the risk neutral measure Q and the T-forward measure Q T are identical if and only if the short rate r t is deterministic. Also, show that the instantaneous forward rate is given by where...
Measure each amount given in Problems 1721. a. Container C in ounces b. Container C in milliliters mL 500- 400- 300 200- 100 cups 2 1 -16-ez -14 oz -12 oz -110 oz 8 oz -16 oz -4 oz 2 oz Container C...
Your consulting firm was recently hired to improve the performance of Shin-Soenen Inc, which is highly profitable but has been experiencing cash shortages due to its high growth rate. As one part of...
At its headquarters in Ventura, California, Patagonia's office space feels more like a national park lodge than the main office of a $400 million retailer. It has a Douglas fir staircase and a...
What is the purpose of a project audit? AppendixLO1
A camera of mass 240 g is mounted on a small tripod of mass 200g, assuming that the mass of the camera is uniformly distributed and that the line of action of the weight of the tripod passes through...
Yosko Company budgeted direct materials purchases of $192,130 in January and $138,840 in February. Assume Yosko pays for direct materials purchases 70% in the month of purchase and 30% in the month...
Consider the yield to maturity R(t, T) corresponding to the CoxIngersoll Ross model. Show that [see (7.2.32a,b)] Explain why an increase in the current short rate increases yields for all maturities,...
Recall that show that the forward rate is given by where the stochastic discount factor is defined by B(r, t) = exp ) = exp(- [* F(t, u) du) = E'o[exp(- [ r(u) du)].
(a) Using $q_{0.10}=3.921$ for the Tukey HSD method, compare the strength of the 5 linen threads in Exercise 12.23 . (b) Use the Bonferroni confidence interval approach on page 411, with...
Obtain the phase trajectories for a system governed by the equation \[\ddot{x}+0.4 \dot{x}+0.8 x=0\] with the initial conditions $x(0)=2$ and $\dot{x}(0)=1$ using the method of isoclines.
Indicate whether each of the following accounts normally has a debit balance or a credit balance. a. Land b. Dividends c. Accounts Payable d. Unearned Revenue e. Consulting Revenue f. Salaries...
Indicate whether each of the following accounts normally has a debit or credit balance. a. Common Stock b. Retained Earnings c. Land d. Accounts Receivable e. Insurance Expense f. Cash g. Dividends...
Match each of the items in the left column with the LO5, 6 appropriate annual report component from the right column: 1. The company's total liabilities 2. The sources of cash during the period 3. An...
Allegra Company has sales of $$167,000$ and a bicak-even sales point of $$123,000$. Compute Allegra s margin of safety and its margin of safety ratio.
Prove the Jacobi identity (u x v) x w + (v x w) x u + (w x u) x v = 0.
Which of the following is NOT a magnetic dipole when viewed from far away? a) A permanent bar magnet. b) Several circular loops of wire closely stacked together with the same current running in each...
List and describe the technologies used in this case study.
In what sense are U.S. farms now digital firms? Explain your answer.
How is information technology changing the way farmers run their business?
Read the following and then answer the questions below:September 12: A Brisbane business offers by letter to sell 500 tyres to a New Zealand company. The Brisbane company does not specify a method of...
Fred returns home from work one day to discover his house surrounded by police. His wife is being held hostage and threatened by her captor. Fred pleads with the police to rescue her and offers...
Would like you to revisit one of these. Consideration must be clear and measurable.if you can't measure it then how can you show it has / has not been done?How can you sue someone for breach of...

Consider the HullWhite model where the short rate process follows where Z t is a Brownian process

Question:

dr = [(t) art] dt + o dZt, -

Step by Step Answer:

Mathematical Models Of Financial Derivative

Students also viewed these Business questions