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 order The 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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