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Convertible Bonds with Call Notice Periods

Convertible Bonds with Call Notice Periods. SONAD 2003 Friday, May 2. Convertible Bonds with Notice Periods. Andreas Grau (agrau@uwaterloo.ca) Peter Forsyth (paforsyth@elora.uwaterloo.ca) Kenneth Vetzal (kvetzal@uwaterloo.ca). Goals.

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Convertible Bonds with Call Notice Periods

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  1. Convertible Bonds with Call Notice Periods SONAD 2003Friday, May 2

  2. Convertible Bonds with Notice Periods Andreas Grau (agrau@uwaterloo.ca) Peter Forsyth(paforsyth@elora.uwaterloo.ca) Kenneth Vetzal(kvetzal@uwaterloo.ca)

  3. Goals • Build a precise model of convertible bonds with notice periods • Evaluate the effect of a notice period for • the optimal call strategy • the value of the convertible bond • Evaluate the effect of suboptimal call strategies

  4. Goals • Build a precise model of convertible bonds with notice periods • Evaluate the effect of a notice period for • the optimal call strategy • the value of the convertible bond • Evaluate the effect of suboptimal call strategies

  5. Goals • Build a precise model of convertible bonds with notice periods • Evaluate the effect of a notice period for • the optimal call strategy • the value of the convertible bond • Evaluate the effect of suboptimal call strategies

  6. Goals • Build a precise model of convertible bonds with notice periods • Evaluate the effect of a notice period for • the optimal call strategy • the value of the convertible bond • Evaluate the effect of suboptimal call strategies

  7. CB Background • CB is a bond with the option to convert it into shares • Interesting for issuers with poor credit rating (start-up company) • Same return, but lower risk as stocks

  8. CB Background • CB is a bond with the option to convert it into shares • Interesting for issuers with poor credit rating (start-up company) • Same return, but lower risk as stocks

  9. CB Background • CB is a bond with the option to convert it into shares • Interesting for issuers with poor credit rating (start-up company) • Same return, but lower risk as stocks

  10. CB Background • CB is a bond with the option to convert it into shares • Interesting for issuers with poor credit rating (start-up company) • Same return, but lower risk as stocks

  11. CB features Company xy - Convertible bond - Amount issued Face value F Conversion ratio k Coupon payments ci Maturity T Options Put price Bp Call period starting at time ts Call price Bcl Trigger price, Notice period Tn,

  12. CB features Company xy -Stock- Volatility s Dividends Di Company xy - Convertible bond - Amount issued Face value F Conversion ratio k Coupon payments ci Maturity T Options Put price Bp Call period starting at time ts Call price Bcl Trigger price, Notice period Tn,

  13. CB features Company xy -Stock- Volatility s Dividends Di Company xy - Convertible bond - Amount issued Face value F Conversion ratio k Coupon payments ci Maturity T Options Put price Bp Call period starting at time ts Call price Bcl Trigger price, Notice period Tn, Risk free rate r

  14. CB models – no default

  15. CB models – no default Time=T V S

  16. CB models – no default V S

  17. CB models – T&F Kostas Tsiveriotis and Chris Fernandes 1998: Valuing Convertible Bonds with Credit Risk

  18. CB models – T&F V S

  19. CB models – AFV Elie Ayache, Peter A. Forsyth, and Kenneth R. Vetzal 2002: Next Generation Models for Convertible Bonds with Credit Risk

  20. V S CB models – AFV

  21. stop call call stop call ti-2 continue stop ti ti-1 continue continue ti+1 Notice periods

  22. call ti continue Notice periods stop call stop call ti-2 continue stop ti-1 continue ti+1

  23. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call ti continue

  24. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call ti continue

  25. call ti continue Notice periods stop call stop call ti-2 continue stop call ti+1 continue ti ti+1 continue

  26. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call V ti Time= ti+1 continue S

  27. stop call call stop call ti-2 continue stop ti ti+1 continue continue V ti+1 Time = ti+1 S Notice periods call ti continue

  28. stop call call stop call ti-2 continue stop ti ti+1 continue continue V ti+1 Time = ti+1 S Notice periods call ti continue

  29. stop call call stop call ti-2 continue stop ti ti+1 continue continue V ti+1 Time = ti+1 S Notice periods V Time= ti+Tn call S ti continue

  30. V Time = ti+Tn stop call call stop call ti-2 continue stop ti ti+1 continue continue S V ti+1 Time = ti+1 S Notice periods call ti continue

  31. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S V ti+1 Time= ti+1 S Notice periods call ti continue

  32. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S V ti+1 Time = ti+1 S Notice periods Time = ti Time = ti call ti ti continue

  33. V V stop call call stop call ti-2 continue stop ti ti+1 continue continue S S ti+1 Notice periods Time = ti Time = ti call ti ti continue

  34. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S ti+1 Notice periods Time = ti Time = ti call ti ti continue

  35. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S ti+1 Notice periods Time = ti call ti continue

  36. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S ti+1 Notice periods Time = ti stop call ti continue ti

  37. V stop call call stop call ti-2 continue stop ti ti+1 continue continue S ti+1 Notice periods Time = ti call ti continue

  38. V stop call call call stop call ti-2 continue stop ti ti ti+1 continue continue continue S ti+1 Notice periods Time = ti Vc,ti call ti continue ti continue V S*

  39. V stop call call call stop call ti-2 continue stop ti ti ti+1 continue continue continue S ti+1 Notice periods Time = ti call ti continue ti continue V

  40. V stop call call call stop call ti-2 continue stop ti ti ti+1 continue continue continue S ti+1 Notice periods call ti continue Time = ti ti continue V

  41. stop call call call stop call ti-2 continue stop ti ti ti+1 continue continue continue ti+1 Notice periods call ti continue ti continue

  42. stop call call call stop call ti-2 continue stop ti ti ti+1 continue continue continue ti+1 Notice periods call ti continue ti continue

  43. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call ti continue ti continue

  44. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call ti continue ti continue

  45. stop call call stop call ti-2 continue stop ti ti+1 continue continue ti+1 Notice periods call ti continue ti continue

  46. call ti continue Notice periods stop call call stop call ti-2 ti continue continue stop ti+1 ti continue continue ti+1

  47. call ti continue Notice periods stop call call stop call ti-2 ti continue continue stop ti+1 ti continue continue ti+1

  48. Mathematical model

  49. Company xy - Stock – Market capitalization 10,000M Implied volatility 20% Dividends 2 once a year, immediately after the coupon Example CB Company xy - Convertible bond – Amount issued 100M Face valueF100 Conversion ratiok 1 Coupon paymentsci2, semi-annually Maturity T5 years Options Call period starting at year 1 Call priceBcl 140 Notice periodTn 30 days Capital market - Bonds – Term structure of risk free rate: Flat, 5% continuously compounded

  50. Example: Effect on value Notice periodTn = 30 days V S

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