Financial Markets and Derivatives
Part III - Swaps
Exercise Nb1
A speculative agent uses Interest Rate Swaps for speculating on future evolution of interest rates. At date 0,
he signed an interest rate swap receiving 8% and paying EURIBOR 3 Months every quarter for 5 years.
We assume that all interest rates are equal (flat yield curve). What is the level at date 0 of interest rates?
What is the agent’s speculative viewpoint?
Ten months later, the interest rates quote 6.50% for all maturities. The EURIBOR 3 Months observed exactly
one month ago was 7.55%. What is the new value of the swap signed at initial date 0? What operation
should the agent take, in order to lock his profit (or loss)?
Exercise Nb2
A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it
receives 10% per annum and pays 6-month LIBOR on a principal of €10 million for 5 years. Payments are
made every 6 months. Suppose that company X defaults on the sixth payment date (end of year 3) when the
interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the
financial institution? Assume that 6-month LIBOR was 9% per annum half way through year 3.
Exercise Nb3
A financial institution borrowed 100 M€ with fixed interest rate 8% (with payment every quarter like the
Euribor 3 months, maturity 3 years and in fine reimbursement of the principal). In order to pay a floating
rate, she signed an interest rate swap with a market maker for 3 years, with fixed rate 8%.
One year and a half later, let us assume that the financial institution bankrupts, before paying the coupons.
The interest rate is then 10%. What are the losses (or gains) for the market maker who signed the swap
contract? What are the losses (or gains) for the initial lender? Explain why the default risk on a swap is
considered as much lower than a loan.
Exercise Nb4
An issuer needs principal to finance a loan (for a client) of 100M€ with floating rate: yearly payment of the
EURIBOR 1 YEAR + 20 bp, and maturity 3 years.
The issuer decides to issue a 3 years fixed coupon bond to get the principal. Because of its good rating
compared with the interbank swap market, the issue can take place with a positive margin for the issuer of
10bp per annum (meaning that the actual rate of the bond is 10bp lower than the swap rate with same
maturity).
a)
Knowing that the issuer can sign a swap with a financial intermediary (for example a swap market
maker) and that the bid offer spread (meaning the margin for the market maker) is 10 bp per annum, explain
how the issuer can solve his problem.
b)
Describe the respective positions of the four agents (borrower, issuer, lender – i.e. buyers of the
bond, and swap counterpart), as well as their respective exposures to interest rate risk.
Numerical Application: mid swap interest rates quote 7%.
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