Variable Strike Bermudan Swaptions (HW-Tree) |

**Variable Strike Bermudan Swaptions (HW-Tree)**

**HWTree_BermReceiverSwaption(argument list…)**

**HWTree_BermPayerSwaption(argument list…)**

These functions return the value per $1 notional (e.g. 0.03 means 3% of notional) of Bermudan Put (Payer) and Call (Receiver) swaptions, using the Hull-White trinomial tree model. When exercised, the holder of the option enters into a swap with a predetermined start and end date. Accruals begin on the swap start date (if exercised before the swap start date) or on the exercise date (if exercised past the swap start date). The functions use the following arguments:

Argument |
Description |
Restrictions |

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

Exercise_Dates |
array of exercise dates | strictly ascending order; the last date must be <= the swap maturity date |

Exercise_Rates |
array of strike rates corresponding to Exercise_Dates array (constant swap rates that are entered into if swaption is exercised) | > 0 |

Notice_Days |
minimum notice, in days, required to exercise swaption | >= 0 |

Swap_Start_Date |
beginning of underlying swap | valid Excel date number |

TIM |
length of underlying swap, in months | > 0 |

Fixed_freq |
number of fixed-side payments per annum | 1, 2, 4, or 12 |

Yr_Basis |
year basis used in determining payments | 360 or 365 |

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

Date_Convention |
business date convention | 0 = no adjustment 1 = Following business day 2 = Modified following 3 = Previous |

Tree_Steps |
number of steps in trinomial tree BETWEEN FIRST AND LAST 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) |

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 |

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 (e.g. six percent entered as 0.06) corresponding to Zero_Dates | > 0 |

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

Bucket_Start |
beginning 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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