Consider the linear SDE that represents the dynamics of a security price dSt 01 Stdt 0 5 StdWt With S0 1 given Suppose a European call option with expiration T 1 and strike K 1 5 is written on this security Assume that the risk free interest rate is 3 (a) Using your computer, generate 1hv normally distributed random variables with mean zero and variance 2 (b) Obtain one simulated trajectory for the St Choose t 2 (c) Determine the value of the call at expiration (d) Now repeat the same experiment with five uniformly distributed random numbers with appropriate mean and variances (e) If we conducted the same experiment 1000 times would the calculated price differ significantly in two cases Why (f) Can we combine the two Monte Carlo samples and calculate the option price using 2000 paths

Question: Consider the linear SDE that represents the dynamics of a security price: dSt = .01 Stdt + 0.5 StdWt With S0 = 1 given. Suppose

Consider the linear SDE that represents the dynamics of a security price:

dSt = .01 Stdt + 0.5 StdWt

With S0 = 1 given.

Suppose a European call option with expiration T = 1 and strike K 1.5 is written on this security. Assume that the risk-free interest rate is 3%.

(a) Using your computer, generate 1hv normally distributed random variables with mean zero and variance √2.

(b) Obtain one simulated trajectory for the St. Choose ∆t = .2.

(d) Now repeat the same experiment with five uniformly distributed random numbers with appropriate mean and variances.

(e) If we conducted the same experiment 1000 times would the calculated price differ significantly in two cases? Why?

(f) Can we combine the two Monte Carlo samples and calculate the option price using 2000 paths?

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

dS t 01S t dt 05S t dW t a see MATLAB program below b see MATLAB program below c A MATLAB program below generates 5 normally distributed random variab... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

41-B-F-F-M (45).docx

120 KBs Word File

Students Have Also Explored These Related Finance Questions!

Consider the linear SDE that represents the dynamics of a security price: dSt = 0.01Stdt + 0.05StdWt with S0 = 1 given. Suppose a European call option with expiration T = 1 and strike K = 1.5 is...

A researcher finds evidence of a security price reaction to an item of accounting information during a narrow window of three days surrounding the date of release of this information and claims that...

Find the price of a 3-month European call option with K = 100, r = 0.05, S(0) = 100, u = 1.1 and d = 0.9 in the binomial model, if a dividend amount of D = $5 is to be paid at time = 1.5 months. Use...

(a) Given a correlation matrix A, 1.0 0.5 0.2 A 0.5 1.0 -0.4 0.2 -0.4 1.0 perform a Cholesky decomposition of the matrix A, which is a decomposition of the form A = LL", when A is symmetric and...

Need help with the 70 multiple choice questions for final exam - if you can, please provide explanation for harder questions. A s ae o . s h r d n. . Surname: ______________________ Q1 Given names:...

Looking for assistance in Finance HW..... I ONLY Need the FORMULASin the function ribbon (for the answers that I already have, which are attached below) Please advise if you can assist and provide...

I would like to know if someone can assist with inputting the formulas into the Excel spreadsheets..... Answers are provided, however, the formulas were omitted. Week 9 Chapter 21: Problems 3(a-e),...

Hi...tutors. 20. Your current portfolio consists of three assets, the common stock of IBM and GM combined with an investment in the riskless asset. You know the following about the stocks (p,,...

Hi, I am doing a project for derivatives class and I have some questions about a regression and Monte Carlo simulation that I need to come up with. So the goal is to hedge against CDS instruments by...

Compute the forward delta of a call option based on the normal formula. (The price is given in Section 1.2.4.) Contrast this with the forward delta for an at-the-money (i.e. forward = strike) call...

What are advantages and disadvantages of having the euro as a common currency in the European Union?

Manufacturing and selling drugs that claim to reduce an individuals cholesterol level is big business. A company would like to market their drug to women if their cholesterol is in the top 15%....

For a given thange in interest rates, the prices of long - term bonds will change less than the prices of short - term bonds. True Fatse

(a The total number of binding sites for the macromolecle B is number) The total number of binding sites for the macromolecule C is (a number) The macromolecule that exhibits the strongest binding to...

Q1. As the production planner for Xiangling Hu products, Inc, you have been given a bill of material for a bracket that is made up of a base, two springs, and four clamps. The base is assembled from...

According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by NW = 21.26t 2 - 330.62t + 2155, Where t is the number of years after...

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining...

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the...

The following exercises are based on the JC Consulting database. What is the primary key field for the Employees table? a. EmployeeID b. HireDate c. Salary d. LastName

Consider the following SDE that governs asset prices in our model: dSt = Stdt + StdWt (24.59) Assume that the risk-free interest rate is 3% and that there are no dividends in the model. Further,...

Knowing the log likelihood equation in the Kalman filter given by Eq. (25.67), use it to estimate the parameter of the linear model from the example done in the chapter.

To see the impact of the choice of the objective function on parameter set obtained from calibration to the same data set,we redo the example done in this chapter under various different objective...

D Question 10 1 pts Let sample space be all students in a College. First event be all freshmen from the college. n(E)= 900 ( No need to list who they are now) Second event be all girls from the...

For this question I also am having trouble finding and computing the lower and upper bound values Use the given statistics to complete parts (a) and (b) Assume that the populations are normally...

Subject - Financial Risk Management 1. Durant Fire Insurance has a retention limit of BD 100,000 and ceded the remaining BD 200,000 to Cury Fire Insurance Company. Considering the reinsurance...