Jamie Ly
April 30, 2009
220

# Swaptions

A description of what swaptions are and how they were used by the Massachusetts Turnpike Authority.

April 30, 2009

## Transcript

1. Swaptions
& the
Massachusetts Turnpike Authority
Fixed Income Analysis
Class Project
April 28, 2009

2. What Are Swaps?
● The most common are interest rate swaps
○ Floating rate swapped for fixed rate.
● Notional amounts
Fixed Floating
AAA 4.0% 6-m LIBOR + 0.3%
BBB 5.2% 6-m LIBOR + 1.0%
● Credit Risks

3. What Are Swaptions?
● Option on a swap
● European Swap Options or Swaptions
● Interest Rate Option like caps/floors
● Use to hedge against interest rate increases
● Alternatives:
○ Forward/deferred swaps

4. Swaption Example
After 6 months...

5. Swaption Valuation Using Black Model
● L: Notional amount
● T: When the swap begins
● n: The period of the swap
● m: Payments annually
● σ: volatility of forward swap rate
● s_k: Fixed rate of swap
● s_t: Swap rate for n-year swap starting at T
● s_0: current swap rate
● T_1, T_2, ..., T_mn: Swap payment dates
● P(0, T_i): Payoff factor at date T_i
● N(x): Cumulative normal distribution of random variable x

6. Value swaption paying fixed rate:
● L: Notional amount
● T: When the swap begins
● n: The period of the swap
● m: Payments annually
● σ: volatility of forward swap rate
● s_k: Fixed rate of swap
● s_t: Swap rate for n-year swap starting at T
● s_0: current swap rate
● T_1, T_2, ..., T_mn: Swap payment dates
● P(0, T_i):Payoff factor at date T_i
● N(x): Cumulative normal distribution of random variable x
The following formulas and examples are from (Hull 2007)

7. Swaption Simplified Calculation
where...
Pay fixed:

8. Swaption Calculation
● s_k = 6.2% (fixed rate of swap)
● s_0 = 6.09% (LIBOR yield is 6%/annum, continuous
compounding)
● n = 3 (3-year swap)
● T = 5 (starts in 5 years)
● σ = 20% (volatility of forward swap rate)
● m = 2 (semi-annual payments)
● \$100 (Principal/Notional Amount)

9. The value of the swaption is \$2.07.

10. Swaption Calculation
● s_k = 4.75% (fixed rate of swap)
● s_0 =5.3201% * 68% (68% 1-m LIBOR) LIBOR yield is 6%
/annum, continuous compounding)
● n = 35 (3-year swap)
● T = 5.5 (starts in 5 years)
● σ = 10% (volatility of forward swap rate)
● m = 2 (semi-annual payments)
● \$207,665,000 (Principal/Notional Amount)

11. The value of the swaption is \$2,013,694.

12. Using Trees to Value Swaptions
Cash flows of
original swap from
t = 0 to t = 1.5 Exercise

13. Using Trees to Value Swaptions

14. Max ( CF, 0 )

Authority (MTA)
● Two highway systems: MassPike and
Metropolitan Highway System (MHS)
● 138-mile long, from MA to NY
● In 1997, the MA government made the
MTA in charge of overseeing
construction of Boston's Big Dig.
● MTA grosses about \$170 million per
year
● Issued \$2.3 billion in 3 series bonds to
finance project
○ accelerated payments began in 2009

16. Financial pressures
● Escalating costs (health, property, utility insurance
● Underforecasted revenues
● Delayed toll increases
● Related debt service
● Center artery/Tunnel (CA/T) (Big Dig) Expenses
● Repair, investigation, remediation

17. Swaptions Entered into by the MTA
● Serious financial pressures led to the MTA entering into
swaption agreements.
● Purpose of the swaptions:
○ additional revenue source that allowed them to:
■ avoid the need for a toll increase in 2002 to 2008
■ achieve a 1.35 coverage ratio
■ provide a modest capital program
■ fund the Fast Lane discount program
■ to offset the fixed-rate bonds they issued
(UBS \$29M,Lehman \$35M)
● But assumed risks for the next 35 years!

18. UBS Swaptions
● Executed in May 2001
● Five fixed-rate payer swaptions, with notional amount
totaling \$800 million
● 35 years
● MTA is the fixed-rate payer
● MTA pays UBS fixed rates of 4.75%, 4.875%, and 5%, and
receives 68% of one-month LIBOR from UBS.
● Cost of termination: \$400 million

19. Lehman Brothers Swaptions
● Executed in November 2002
● Five fixed-rate receiver swaptions, with notional amount
totaling \$800 million
● 35 years
● MTA is the fixed-rate receiver
● Cost of termination: \$30 million
● Were meant to offset the five UBS swaptions

2Flibor_rates_history-chart-graph.
htm&ei=C8PeSaLsC9XwnQeRz5W1CQ&usg=AFQjCNHqhjAsmtLnvpim3KSXeVEOwHXumA&sig2=RmL0elOoX13j
mNJPE4pmUA
UBS
exercises
swaptions
2
2
1
UBS
swaption
executed
Lehman
swaption
executed

21. Problems from the UBS Swaptions
● Exercised in Jan 2008, Jul 2008, Jan 2009
● MTA pays UBS fixed rates of 4.75%, 4.875%, and 5%, and
receives 68% of one-month LIBOR from UBS.
○ One-month LIBOR is now ~0.33%, compared to 4.56% three
months ago. This means the MTA is receiving only 0.2244%.
● The swaptions have increased MTA's fixed rate liabilities
and is estimated to require \$24 million in annual expenses
by 2010.
● Massachusetts government temporarily backed the MTA
with a "general obligation" which expired in January 2009
○ MA government has a stronger credit rating (AA) than the MTA

22. Problems (continued)
● \$12.1 million deficit in budget as of Jan 2009
● Has and will need to increase tolls ranging from a 50%
increase in some areas to double in others. Expected to
result in \$90 million additional revenue
● Reduced toll collector staff from 375 to 275 in December,
plans to terminate another 80
● At current bond rating, borrowing capital is impossible

23. Problems (continued)
● Bonds and swaps do not match
○ Now must pay \$2 million per month in additional interest
costs
● Going to refinance the bonds to variable rate to better match
the bonds to the swaps:
○ Citi \$229 million
○ JP Morgan \$207 million
○ Morgan Stanley \$185 million
○ Merrill Lynch & Co. \$185 million
● Terminated the Lehman Brothers swaptions (which were
never exercised) to prepare for the refinancing in December
2008 and paid Lehman \$3.4 million fee
● Ongoing litigation - MTA disputes the trigger of the
termination fee

24. Termination Fee Triggered
● Termination fee of \$400 million was allegedly triggered
when MTA’s insurer, Ambac Assurance Corporation, was
downgraded by S&P and Moody's during the same month.
○ 9/10/2008 Fitch places MTA bonds on Rating Watch Negative
○ In November, 2008, Moody's downgraded Ambac from Aa3 to
Baa1
○ In November 2008, S&P assigned a negative outlook and
proposed downgrade of Ambac from A to AA
○ UBS wrote a letter to MTA notifying of the termination fee
trigger

25. References
● Fabozzi, Frank. Bond Portfolio Management. Hoboken: Wiley & Sons, Inc., 2001
● "Fitch Puts Massachusetts Turnpike Authority's Metro Highway System Revs on Watch Negative." Reuters. 9 Sep 2008.
28 Mar 2009. .
● Hull, John C.. Options, Futures, and Other Derivatives. 6. New Delhi: Prentice-Hall, 2007.
● "Massachusetts Turnpike reducing toll collectors from 375 to 275." Tollroad News. 12 Dec 2008. 18 Mar
2009. .
● "Fitch Comments on Massachusetts Turnpike Auth MHS Swaptions." Business Wire. 19 Dec 2008. 18 Mar
2009. .
● "Toll Increase - Frequently Asked Questions." MTA - Turnpike News. 15 Dec 2008. 18 Mar
2009. .
● "Fitch Affirms MA Turnpike Auth MHS Sr. Bnds at 'BBB+'/Sub. Bnds at 'BBB'; Stable Outlook." The Free Library by
Farlex. 28 Jul 2005. 18 Mar 2009. com /Fitch+Affirms+MA+Turnpike+Auth+MHS+Sr.+Bnds+at+%27BBB%2B%27%2FSub.+Bnds+at...-
a0134595894>.
● Kaske, Michelle. "MassPike Swap Payment a Looming Threat." The Bond Buyer. 14 Jan 2009. 18 Mar 2009. //www.bondbuyer.com/article.html?id=20090113QT0BC3WK>.
● "Massachusetts Turnpike Authority, Financial Statements, Required Supplementary Information, and
Supplementary Schedules, December 31, 2003 and 2002." KPMG. 17 Sep 2004.
● "Transportation Finance in Massachusetts: An Unsustainable System. Findings of the Massachusetts Transportation
Finance Commission." 28 Mar 2007.
● "Massachusetts Turnpike Authority Request for Proposals. Legal Services for Potential Claim(s) Against Investment
Bank/Swap Counterparty, Financial Advisor, Bond Insurer and/or Rating Agencies." 29 Jan 2009.
● "Ehrlich: Understanding 'swaptions' coming down the Pike." The Milford Daily News. 26 Mar 2009. 10 Apr 2009. //www.milforddailynews.com/opinion/x759739191/Ehrlich-Understanding-swaptions-coming-down-the-Pike?view=print>.
● http://www.wsjprimerate.us/libor/libor_rates_history.htm