Variable-coupon American & Bermudan Bond Options (HW-Tree) |

**Variable-coupon American & Bermudan Bond Options (HW-Tree)**

**HWTree_BondAmerCallVar(argument list…)**

**HWTree_BondAmerPutVar(argument list…)**

**HWTree_BondBermCallVar(argument list…)**

**HWTree_BondBermPutVar(argument list…)**

These functions return the values of American and Bermudan call and put options on variable coupon bonds with varying strike prices using the Hull-White trinomial tree interest rate model. The functions use the following arguments:

Argument |
Description |
Restrictions |

Val_Date |
valuation date (e.g. today) | valid Excel date number |

Bond_Settlement_Lag |
number of business days until settlement for bond transaction made on Valuation_Date | >= 0 |

Bond_Maturity |
bond maturity date | > Valuation_Date (with settlement lag) |

Freq |
number of bond coupons per annum | 1, 2, 4, or 12 |

DCB |
day count basis | 0 = 30/360 (US) 1 = act/act for CAD/US T-Bonds 2 = act/360 3 = act/365 4 = 30/360 (European) |

Coupon_Dates |
array of bond coupon dates | First element must be the last coupon date before the settlement date, or an even older coupon, and last element must be the maturity date of the bond. Dates must be in ascending order, and consistent with the coupon frequency and maturity date. |

Coupon_Rates |
array of bond coupon rates, as annualized rates, in decimal form (e.g. six percent entered as 0.06) | >= 0, and corresponding to the Coupon_Dates array |

Last_Exer_Date |
is the final option exercise date; is used to provide a final exercise date for American options (see Strike_Dates) | < Bond_Maturity |

Notice_Days |
the number of days needed to give notice for option exercise | >= 0 |

Strike_Dates |
an array of exercise dates for the option; for American options, it is the date the strike price changes (steps up/down) to the next strike rate (i.e. strike price is in effect from the strike date to the next one, or to the Last_Exer_Date | ascending order |

Strike_Prices |
an array of option strikes per $100 par, corresponding to the strike dates | > 0 array must be same size as Strike_Dates |

Holidays |
array of holiday dates | valid Excel date numbers strictly ascending order |

Short_Rate_Vol |
annual standard deviation of the short rate of interest, in decimal form | > 0 |

Reversion_Rate |
mean reversion rate of the short rate of interest, in decimal form | >= 0 |

Tree_Steps |
number of steps in trinomial tree BETWEEN THE NEXT AND FINAL EXERCISE DATES | > 0, typically 50 to 100, although this should be lowered if the exercise period is a small fraction of the life of the option (otherwise too many tree steps in total) |

Zero_Dates |
array of zero coupon curve dates | strictly ascending orderThe first date of this array must be Valuation_Date |

Zero_Rates |
array of continuously compounded riskless rates in decimal form corresponding to Zero_Dates | > 0 |

OAS |
parallel shift of the zero curve in decimal form | |

Bucket_Start |
start of bucket for zero curve shifts | set to 0 if curve shift is not desired |

Bucket_End |
end of bucket for zero curve shift | >= Bucket_Start |

Bucket_Shift |
parallel shift of the zero curve between Bucket_Start and Bucket_End in decimal form | set to 0 if curve shock is not desired |

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