1. Calibrate the LIBOR closing prices you have been given to a Vasicek Model using the techniques described in [?, Section 7] [Assume 220 trading days].
2. Based on your results to (1) plot the yield curve for maturities up to 20 years assuming that r0, the current LIBOR quote is
(a) 1.5%,
(b) 3.0%,
(c) 6.0%.
3. Using the parameters identified in (1) develop a Monte-Carlo simulation of LIBOR using the Vasicek model.
(a) Describe the simulation method (exact or discretised) and explain why you chose that method.
(b) Explain how you will handle unrealistic rates.
(c) Comment on the accuracy of your simulated results in relation to theoretical results.
You need to submit your code.
4. Use the simulation method developed in (3) to produce a single set of 220 consecutive daily LIBOR quotes based on the results of (1) and calibrate this simulated data to the Vasicek model (i.e. repeat (1) but on this data). What do you observe? Give an order of magnitude number of quotes that would give a reasonable approximation (i.e within 10% of all parameters)?
5. Calculate the price of a bond option that pays, at time S
max {BST - K, 0}
where BST is the time s price of a t-maturity discount bond, S = 2; T = 5; K = 0:9 (i.e. K is 90% of face) and r0 = 3:0% using
(a) The parameters you derived in (1)
(b) Using κ= 0:25; θ = 3:5%; σ = 0:8:
which are the parameters used to create the LIBOR quotes you have been given. And give a percentage difference between the quotes. Comment on this result.
6. Comment on what you have learnt so far on this project.
7. Assuming LIBOR follows the Vasicek stochastic process, following the parameters you have estimated, calculate the value of a swaption that gives the holder the right to pay 3.0% in a 3-year swap starting in 5 years. Payments are made semi -annually and the notional principle is $100 million.
You need to deliver a result, any code you use and a description of the method and theory underlying your approach.
8. Calibrate the LIBOR closing prices you have been given to a CIR Model using the techniques described in [?, Section 9] [Assume 220 trading days]. In this case the OLS results are not expected to be the same as MLE results and you should comment on your choice of method (both methods are acceptable in this project).
9. Assuming LIBOR follows the CIR model, using the parameters you have estimated, calculate
(a) The price of a bond option that pays, at time S
(b) max {BST - K, 0}
where BST is the time s price of a t-maturity discount bond, S = 2; T = 5; K = 0:9 (i.e. K is 90% of face) and r0 = 3:0%
(b) The value of a swaption that gives the holder the right to pay 3.0% in a 3-year swap starting in 5 years. Payments are made semi-annually and the notional principle is $100 million.
You need to deliver a result, any code you use and a description of the method and theory underlying your approach.
10. Comment on the difference between the two swaption quotes.
11. Comment on what you have learnt in the second part of the project.
Attachment:- Assignment Files.rar