Consider the linear stochastic differential equation Show that the mean E r(t) is governed by the following deterministic linear differential equation while the variance var(r(t)) is governed by When the results are applied to the CIR interest rate model show that E r(T) r(t) and var(r(T) r(t)) are...

Consider the linear stochastic differential equation Show that the mean E[r(t)] is governed by the following deterministic

Question:

Consider the linear stochastic differential equation

dr(t) = [a(t)r(t) + b(t)] dt + p(t) dz(t).

Show that the mean E[r(t)] is governed by the following deterministic linear differential equation:

d dt -E[r(t)] = a(t) E[r(t)]+b(t), while the variance var(r(t)) is governed by

d dt -var(r(t)) = 2a(t)var(r(t))+p(t).

When the results are applied to the CIR interest rate model:

show that E[r(T)|r(t)] and var(r(T)|r(t)) are given by (7.2.30a,b).

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

Step by Step Answer:

Related Book For answer-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

Determine the length of the crankshaft AB by first formulating a Cartesian position vector from A to B and then determining its magnitude. Given: a = 400 b = 125 θ = 25 deg B
To promote safe driving habits and to better protect its customers, an insurance company offers a discount of between 5% and 20% on renewal insurance premiums to customers who have completed a...
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
In SSL and TLS, why is there a separate Change Cipher Spec Protocol rather than including a change_cipher_spec message in the Handshake Protocol?
Gourmet Specialty Coffee Company (GSCC) is a distributor and processor of different blends of coffee. The company buys coffee beans from around the world and roasts, blends, and packages them for...
What are pipeline slurry systems? How do they function?
The production department of Zunni's Manufacturing is considering two numerically controlled drill presses; one must be selected. Comparison data is shown in the table below. MARR is 10 percent/year....
During 2011, Rooster Company purchased 5,000 shares of Hen Company common stock for $18 per share and 3,200 shares of Egg Company common stock for $21 per share. These investments are intended to be...
Scenario 7:Accountant 7 is the audit manager of a distressed client. Our client is in true financialtrouble and they want our firm to lend them money. Can we?
An extended version of the Vasicek model takes the form (Hull and White, 1990) Let (t) denote the time dependent market price of risk. Show that the bond price equation is given by Suppose we write...
Consider the yield curve associated with the Vasicek model [see (7.2.26)]. where F(t, t + ) is the forward rate and E t Q is the expectation under Q conditional on the filtration F t . Show that the...
List the general characteristics of epithelium, and then describe the basic types of epithelial tissues in terms of specific characteristics and functions.
A project has 3 years of profits of: 25,000, 35,000 and 15,000. The initial investment was 95,000 (with a disposal value of 5,000). What is the Accounting Rate of Return (ARR) on the project?
Sometimes requesting payment or responding to patient inquiries about financial matters can be uncomfortable. Which qualities best describe customer service to you? Cite some examples of how you...
(a) What power contact lens is needed to correct the vision of a person who has a near point of 78.0 cm and allows him to see objects 25.0 cm away? (b) If this person has a normal 8.00 % ability to...
A new manufacturing plant costs $5,500,000 to build. Operating and maintenance costs are estimated to be $41,000 per year, and a salvage value of 25% of the initial cost is expected. The units the...
ina owns a hostel in a large town. She bought a copy machine for $1,700, which has a life expectancy of 40,000 units. In the first year, Tina and her staff copied 800 units. In the second year, they...
The U.S. Department of Agriculture publishes data annually on various selected farm products. Shown here are the unit production figures (in millions of bushels) for three farm products for 10 years...
Big Jim Company sponsored a picnic for employees and purchased a propane grill equipped with a standard-sized propane tank for the picnic. To make sure there was enough propane for all the cooking...
Describe the characteristics of a learning organization.
Describe potential sources of, and ways of managing, work stress .
What kinds of applications are described here? What business functions do they support? How do they improve operational efficiency and decision making?
By making use of the identities z = eLn(z) and Ln(z) = a Ln(z), simplify and evaluate the following expressions: (a) i2 and (b) i". Show all details of work.
Chef needs to prepare 120 portions of steamed cauliflower. Each cooked portion is 3 oz. The vegetable loses 28% of its weight when cooked. Raw cauliflower costs $3.59/lb. How many ounces of raw...
Your company has decided to adopt a NoSQL database management system for storage and processing of big data. You have been asked to investigate alternative NoSQL technologies. (a) Explain the...

Consider the linear stochastic differential equation Show that the mean E[r(t)] is governed by the following deterministic

Question:

dr(t) = [a(t)r(t) + b(t)] dt+ p(t) dz(t).

Step by Step Answer:

Lets start by considering the linear stochastic differential equation SDE given drt atrt btdt ptdZt ...View the full answer

Mathematical Models Of Financial Derivative

Students also viewed these Business questions