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Swaptions

Jamie Ly
April 30, 2009
220

 Swaptions

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

Jamie Ly

April 30, 2009
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  1. Swaptions
    & the
    Massachusetts Turnpike Authority
    Fixed Income Analysis
    Class Project
    April 28, 2009

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

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  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

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  4. Swaption Example
    After 6 months...

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  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

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  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)

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

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  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)

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  9. The value of the swaption is $2.07.

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  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)

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

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

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  13. Using Trees to Value Swaptions

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  14. Max ( CF, 0 )

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  15. About the Massachusetts Turnpike
    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

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

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  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
    ○ Total of $64 million received in additional revenue
    (UBS $29M,Lehman $35M)
    ● But assumed risks for the next 35 years!

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  18. UBS Swaptions
    ● Executed in May 2001
    ● Five fixed-rate payer swaptions, with notional amount
    totaling $800 million
    ● MTA received $29 million premium payment
    ● 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

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

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  20. http://www.google.com/url?sa=t&source=web&ct=&cd=2&url=http%3A%2F%2Fwww.wsjprimerate.us%2Flibor%
    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

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  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

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  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

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  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

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  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
    (likely downgrade)
    ○ 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

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  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

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