Questions about Snowball Swap

Read the HBS case in the packet on “Snowballs in Portugal” and prepare a report addressingthe questions below. On the Canvas site you will find historical data on the 3-month Euriborrate, and on the term-structure of Euro-zone government rates on two different dates.

� Question 1. Using data on 3-month Euribor and, based on the terms shown in Exhibit8, compute the total (undiscounted) amount of net payments MdP was required tomake from the start of the swap through March 13, 2018.

� Question 2. In reality, MdP stopped making payments in 2013 and claimed the swapswere illegal. The case went to trial under British law. Suppose you work for BancoSantander (the counterparty) and you want to assess your exposure to the event thatyou lose in court and the swap is terminated. You will do this by computing the mark-to-market value of the swap as of December 13, 2013 using Monte Carlo simulation.For this purpose, you decide to use the Vasicek model for Euribor. The steps are asfollows.

1. First use the Euro area government yield curve from December 13, 2013 to finda value for the market price of risk that best fits the curve.

– Assume κ = 0.20 and b = 0.0065, and set r0 to the shortest maturity yieldon the curve.

– Next, for a range of r⋆ values, evaluate the functions G0(0, T) and G1(0, T)in Lecture Note 4.2 out to a maturity of T = 30 years. Convert the bondprices into (zero-coupon) rates for each T .

– Compute the absolute average error in fitting the data rates for each r⋆. Thenpick the value that gives you the lowest error.

– (Note that r⋆ is all you need. It’s not necessary to convert it into a λ.)

2. Now using your risk-neutralized model, draw 10000 paths of r from 2013 to 2022using daily time-steps. Along each path, compute the net cash-flows from theswap to/from MdP, cumulate their discounted sum, and then average the resultover all paths. Some things to remember:

– Start the simulations from the r0 value you used in fitting the yield curve. Usethe initial value for spread0 to be the value you computed as of September13, 2013 in Question 1 based on the historical rate.

– At each time-step, t, where there is no cash payment, just increment rt by

adding dr and increment the discount factor DF0,t = e−

∫ t0ru du by multiplying

by e−rt ∆t.

– At time-steps corresponding to cash flows, t = 0, 0.25, 0.5, …, and using thespread value from the previous quarter figure out the net cash-flow due atthat date; multiply it by the discount factor, and add it to the total cash-flowof the path.

– Then use rt to update the spread amount to be paid at the end of the quarter.(You can assume the instantaneous rate is the same as the 3-month rate.)

� Question 3. One of BdP’s argument in court was that the swap was so unfair at thestart that they themselves must have been too unsophisticated to understand it! – andtherefore Santander had committed fraud in selling it to them. To assess this claim,repeat your mark-to-market valuation of the swap as of March 13, 2007.

– Re-estimate r⋆ using the yield curve data provided for March 13, 2007. Nowassume that κ = 0.04 and b = 0.0065.

– Re-do your simulations using the starting r0 on that date (and initial spread = 0).

– Report your valuation as well as the Monte Carlo standard error. (For an accurateprice, you may need more than 10000 paths.)

Is it true that it was a bad deal for BdP from the start? How bad?

� Question 4. Discuss how sensitive your valuation conclusions in Questions 2 and 3are likely to be to your model of interest rates. Are you confident in your choice of theVasicek model and its parameters? Why or why not? What could you do – if you hadmore time – to assess the model or improve it?

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