Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

To answer this question, please start by builiding and calibrating a 1 0 - period Black - Derman - Toy model for the short -

To answer this question, please start by builiding and calibrating a 10-period Black-Derman-Toy model for the
short-rate, ri,j. You may assume that the term-structure of interest rates observed in the market place is:
Period 1,2,3,4,5,6,7,8,9,10
As in the video modules, these interest rates assume per-period compounding. For example, the market-price of a
zero-coupon bond that matures in period 6 is Z06=100(1+.035)6=81.35 assuming a face value of 100.
Assume b=0.05 is a constant for all i in the BDT model as we assumed in the video lectures. Calibrate the ai
parameters so that the model term-structure matches the market term-structure. Be sure that the final error
returned by Solver is at most 10-8.(This can be achieved by rerunning Solver multiple times if necessary, starting
each time with the solution from the previous call to Solver.)
Once your model has been calibrated, compute the price of a payer swaption with notional $1M that expires at
time t=3 with an option strike of 0. You may assume the underlying swap has a fixed rate of 3.9% and that if
the option is exercised then cash-flows take place at times t=4,dots,10.(The cash-flow at time t=i is based
on the short-rate that prevailed in the previous period, i.e. the payments of the underlying swap are made in
arrears.)
Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer
to be 10,456.67, submit 10457.
To answer this question, please continue using the calibrated model from the last question.
Repeat the previous question but now assume a value of b=0.1.
Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer
to be 10,456.67, submit 10457.
Please refer to the material on defaultable bonds and credit-default swaps (CDS) to answer this question.
Construct a n=10-period binomial model for the short-rate, ri,j(i=0,1,2dots9). The lattice parameters are:
r0,0=5%,u=1.1,d=0.9 and q=1-q=12. This is the same lattice that you constructed in
Assignment 5.
Assume that the 1-step hazard rate in node (i,j) is given by hij=abj-12 where a=0.01 and b=1.01.
Compute the price of a zero-coupon bond with face value F=100 and recovery R=20%.
Submission Guideline: Give your answer rounded to two decimal places. For example, if you compute the answer
tPlease answer the following questions:
o be 73.2367, submit 73.24.
image text in transcribed

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Fundamentals Of Corporate Finance

Authors: Jonathan Berk, Peter DeMarzo, Jarrad Harford

5th Edition

0135811600, 978-0135811603

More Books

Students also viewed these Finance questions

Question

13.1 Explain the strategic role of employee benefits.

Answered: 1 week ago