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Swaptions

Jamie Ly
April 30, 2009
140

 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
  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
  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: Receive 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 )

  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
  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
  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!
  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
  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
  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
  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 (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
  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. <http://www.reuters.com/article/pressRelease/idUS188113+09-Sep-2008+BW20080909>. • 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. <http://www.tollroadsnews.com/node/3882>. • "Fitch Comments on Massachusetts Turnpike Auth MHS Swaptions." Business Wire. 19 Dec 2008. 18 Mar 2009. <http://www.allbusiness.com/banking-finance/financial-markets-investing/5973127-1.html>. • "Toll Increase - Frequently Asked Questions." MTA - Turnpike News. 15 Dec 2008. 18 Mar 2009. <http://www.masspike.com/user-cgi/news.cgi?dbkey=313&type=Press%20Release&src=news>. • "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. <http://www.thefreelibrary. 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. <http: //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. <http: //www.milforddailynews.com/opinion/x759739191/Ehrlich-Understanding-swaptions-coming-down-the-Pike?view=print>. • http://www.wsjprimerate.us/libor/libor_rates_history.htm