Derivatives and Risk Management Techniques Project
Computation of the snowball 'spread' and cash flows -
Questions:
1. Why did the company MdP enter into a second swap in 2007?
2. Explain the impact on the interest the company had to pay during the first 2 years of the swap.
3. Explain what happened since to the swap.
4. Describe which 2 to 3 important/relevant features of interest rate dynamics you can recognize in the CIR process (Equation 1).
5. Can you recognize the fatal flaw in the naive discretization (Equation 2)? Describe it.
6. Write out a formula that does not use words (except variable names) that computes the current quarter's spread as a function of the previous quarter's spread and the current interest rate. Also, report the corresponding Excel formula which you used to implement this in the workbook. For the purpose of this question, leave out the bracketing IF clauses that have to do with 'Nstep' or 'N?x'.
7. Given the dynamics of the short rate and starting values given in the table under scenario 1, compute the approximate Monte Carlo based value of the swap at the original time of entry? (You should press 'F9' a few times to get an idea of the average value)
8. Based on this result alone can you justify MdP entering into the swap?
9. Investigate the spread that determines the payment at the end of the last quarter of the swap's life time. Report the ten lowest and highest spreads in a table.
You can use Excel functions LARGE() and SMALL() for this [2P]. Also investigate the shape of the distribution of payoffs. What are the ten worst, ten best outcomes from the perspective of MdP? Export a table into your report. What is the 95% VaR of this trade? Also report median, standard deviation, skewness and kurtosis.
10. Compute the theoretically possible maximum value of this swap, i.e. what does MdP maximally stand to gain if everything works out in their favor? Also compute the present value of all interest payments that MdP still had to make at that point in time under the original plain-vanilla swap contract. Use the same discount rate which you assumed for the maximum value. What is the magnitude of interest rate savings in percent in the best case?
11. Given these additional results, re-visit the wisdom of entering into this swap by comparing benefits and risks.
12. As mentioned by Matt Levine, it is not clear how to think about the leverage that is built into this snowball swap. Lets construct a second cash flow sheet where we assume that the spread in each period is simply the difference between Euribor and a) 2% on the downside or b) 6% on the upside and c) zero otherwise - multiplied by a factor called 'leverage', with no accumulation and no digi-coupon. What approximate magnitude of 'leverage' is needed to get to the same value ex-ante (press F9 repeatedly for different choices of 'leverage')? Comment on what this equivalent leverage factor means for the risk that MdP is taking on (ex-ante).
13. In September 2013 (scenario 2), MdP had enough, stopped paying and started legal action. Using the alternative values in the table, in particular starting with a current spread of 40%, what is the value of the swap now? Also, re-calibrate your leverage factor to see what the equivalent leverage would be now with the snowball contract being massively under-water.
Implied Volatilities & Volatility Smiles -
Questions:
1. Explain why it makes sense that the target cell in the Solver minimization references the control variate estimate of the American Put option instead of the value as implied by the tree alone.
2. Use Solver to ?nd the implied volatilities for put options with strike prices between $67.50 and $97.50 in steps of $5 (i.e. you can leave some options out) whenever they are available for a given option chain. Save your implied volatility results in a separate worksheet along with maturity and strike price or add them to the data ?le. Once you have done this for all 3 option chains, you will need to create a graph in Excel that depicts the three volatility smiles as a function of strike price.
3. Describe what you see in that graph [3P]. What would you expect to see in a Black-Scholes world [2P]? Which option chain exhibits the steepest volatility smile and why exactly is this the case?
Early Exercise Premium -
Questions:
1. Fix the risk-free rate at 4.0%. Now let the spreadsheet compute results for all possible combinations as you vary the strike price in steps of $6 between $48 and $72 and time to maturity between 182, 365 and 548 days. Enter a start date of your choice and then enter in the field for expiration date =settlement+182 for the first maturity. Submit the table and the graph.
2. Fix the time to maturity at 365 days. Now vary the strike price as before and also vary the interest rate between 1.0%, 4.0% and 7.0%. Submit the table and the graph.
3. Describe briefly how the EEP depends on the parameters we varied in this exercise.
Attachment:- Assignment Files.rar