1 / 40

Bonds and Swaps

FIN285a: Lecture 5.1a Fall 2008. Bonds and Swaps. Outline. Coupon bonds Currency swap Fixed/floating swaps. Software. bondvar.m bpswaphist.m bpswapbs.m fixfloat.m. Bond Pricing: Assumptions. Flat term structure Yields Geometric random walk Rate = Tbond + 5% (risk spread)

DoraAna
Download Presentation

Bonds and Swaps

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FIN285a: Lecture 5.1a Fall 2008 Bonds and Swaps

  2. Outline • Coupon bonds • Currency swap • Fixed/floating swaps

  3. Software • bondvar.m • bpswaphist.m • bpswapbs.m • fixfloat.m

  4. Bond Pricing: Assumptions • Flat term structure • Yields • Geometric random walk • Rate = Tbond + 5% (risk spread) • Volatility = 1.75*tbond volatility

  5. Bond Structure • Principal = 1000 • Coupon = 8% = 80 (starting in 1 year) • Maturity = 3 years • Problem: • Find VaR and ETL over 1 year period

  6. Matlab Program • bondvar.m • Features • Government bond data file • Aggregate 12 months to get 1 year changes

  7. Outline • Coupon bonds • Currency swaps • Fixed/floating swaps

  8. Currency Swap • Foreign currency swap • Trade principal and interest in one currency for another • Borrow British pounds, lend US dollars • Structure • Long $ bond • Short BP bond

  9. Valuation of Swap

  10. Simple Swap Example • 1 Year contract • Interest payments at 6 months and 1 year • BP principal = 20 million BP • Payback in 1 year • $ principal = 20 million BP ($/BP)

  11. Coupon Payments • BP coupon : 6 months and 1 year • c(BP) • $ coupon : 6 months and 1 year • c($)

  12. Cash Flow • Today • 20BP, -($/BP)20BP • 6 Month (coupons) • -c(BP) = Libor(BP) + 1% • +c($)=Libor($) + 2% • 12 Month • -20BP-c(BP), ($/BP)20BP+c($)

  13. Cash Flow PictureLet X = $ notional = E($/BP)20Fixed today at current FX rateNote: now transactions neutralize +20 BP +c($) +c($)+X $ -c(BP) -X $ -c(BP)-20 BP 12 Months Now +6 Months

  14. Find 1 Month VaR • Mark to market today (current FX and interest rates)V(t) • Find FX and interest rates 1 month in the future (t+1) • Use historical data and arithmetic returns • Mark to market in one month V(t+1) • Find VaR using P/L = V(t+1)-V(t)

  15. Risk Factors • Exchange rate ($/BP) • r(BP): British interest rate • Flat term structure • r($): US interest rate • Flat term structure

  16. Valuation in US $ (today)

  17. Valuation in US $ (1 month future)

  18. Data Set bp.dat • Date (matlab format) • $/BP exchange rate • R(BP) = 1 Month interbank (London) • R($) = 1 Month eurorate (London) • Source: Datastream

  19. Matlab Code • Historical VaR • bpswaphist.m • Note: impact of FX • Bootstrap values • bpswapbs.m

  20. Multiple Risk Factors • X = % Change [FX r(BP) r($)] • Historical • Use matrix of changes • Keep changes in each component of X together in time

  21. Multiple Risk Factors • X = % Change [FX r(BP) r($)] • Bootstrap • Use matrix of changes • Keep changes in each component of X together in time • Sample X together • Sample command does this (row by row)

  22. Multiple Risk Factors • X = % Change [FX r(BP) r($)] • Bootstrap 2 • Assume independence • Sample separately • xbs = sample(x(:,1),n)

  23. Multiple Risk Factors • X = % Change [FX r(BP) r($)] • Monte-carlo • Assume normality • Estimate mean vector • Estimate variance/covariance matrix • Simulate multivariate normals • Find valuations V(x(t+1))

  24. Multiple Risk Factors • X = % Change [FX r(BP) r($)] • Delta normal • Assume normality • Estimate mean vector • Estimate variance/covariance matrix • Linearly approximate distribution of V(X)

  25. Multi Factor Challenges • Which factors are important? • How do they move together? • Covariances??

  26. Outline • Coupon bonds • Currency swaps • Fixed/floating swaps

  27. Interest Rate Swaps • Pay fixed coupon payments • Receive floating coupon payment (Libor * notional amt.) • or the reverse • Floating rate locked 6 months before payment • Also, dealers arrange and take a spread

  28. Swap Example • Structure • Receiving fixed payments • Paying floats • Semiannual payments • Units: semiannual compounding • 1 year to maturity • Payments in 6 and 12 months

  29. Swap Valuation • Long a fixed rate bond • Valuation: easy • Short a floating rate bond • Valuation: a little tricky, but not bad • Swap value = PV(fixed) - PV(float)

  30. Semiannual Compounding

  31. Bond Specifics • Fixed: • Principal = 1000 • Coupon = 5% (semi-annual) • Maturity = 1 year • Float: • Principal = 1000 • Coupon = Libor (initial = 5%) semi-annual • Maturity = 1 year

  32. Valuing Fixed at Issue

  33. Valuing Float at Issue

  34. Picture of the Float 6 Months 1000(1+r(6)/2) C=1000*r(0)/2 r(0) r(6) Right after coupon is paid PV at r(6)/2 = $1000 Valuation 1 month in the future is easy PV( 1000*r(0)/2 + 1000)

  35. Valuing Float 1 Month in the Future

  36. Valuing Swap (1 Month Future)

  37. Picture of the Float 6 Months 1000(1+r(6)/2) C=1000*r(0)/2 r(0) r(6) Right after coupon is paid PV at r(1)/2 = $1000 Valuation 7 months in the future trickier. Need r(6) for coupon and r(7) for discount.

  38. Valuing Float 7 Months in the Future

  39. Valuing Swap (7 Month Future)

  40. Matlab Code • fixfloatswap.m

More Related