HWTree_AccrualConv() function |

**HWTree_AccrualConv() function**

**HWTree_AccrualConv(argument list…)**

This functions prices an accrual bonds which is convertible at the PAYERS option into a normal pay bond (i.e. coupons at regular frequencies, instead of accruing to a final maturity). The underlying bond may pay a varying coupon rate (e.g. step-up) and have a Bermudan style exercise schedule. The initial notional value is assumed to be $100. When the bond is converted, the difference between the accrued value and $100 is payable immediately, and afterwards the payments are as a normal (step-up) coupon bond, with the $100 notional payable at maturity. If the option is nver converted, the accrued value (interest plus principal) is payable only at maturity. The functions use the following arguments:

Argument |
Description |
Restrictions |

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

Settle_Date |
bond settlement date | valid Excel date number >= Valuation_Date |

Maturity_Date |
bond maturity date | valid Excel date number >= Settlement_Date |

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) |

Coup_Dates |
array of bond coupon dates | First element must be first coupon date of the bond (i.e. AFTER the issue date), and last element must be the maturity date of the bond. This is important as the bond is accruing with an initial notional of $100. Dates must be in ascending order, and consistent with the coupon frequency and maturity date. |

Coup_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 |

Exercise_Array |
an array of indicator values which tells us if the payer can convert to normal pay on this date | = 1 if convertible on a date = 0 if not convertible on a date |

Notice_Days |
minimum notice, in days, required to convert the bond | >= 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 |

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 |

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 |

Steps_per_Coupon |
tree steps per fixed coupon period in the trinomial lattice | > 0 (typically 3 to 10) if there is only 1 exercise period remaining, and the time to exercise is short, a very high value such as 100 should be used, to ensure that the lattice is built |

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