American & European Swaptions (HW-Tree) |

**American & European Swaptions (HW-Tree) **

**HWTree_AmerReceiverSwaption(argument list…)**

**HWTree_AmerPayerSwaption(argument list…)**

**HWTree_EuroReceiverSwaption(argument list…)**

**HWTree_EuroPayerSwaption(argument list…)**

These functions return the value per $1 notional (e.g. 0.03 means 3% of notional) of American/European Put (Payer) and Call (Receiver) swaptions, using the Hull-White trinomial tree model. When exercised, the holder of the option enters into a spot-starting swap with fixed term in months relative to the exercise date. The functions use the following arguments:

Argument |
Description |
Restrictions |

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

Swaption_Maturity |
expiry of swap option | valid Excel date number >= Valuation_Date |

Strike_Rate |
swaption strike rate in decimal form (e.g. six percent entered as 0.06) | > 0 |

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

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

Year_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 | > 0, typically 25-50 |

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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