Complex Callable Bonds (HW-Tree)

Complex Callable Bonds (HW-Tree)

HWTree_CallableBond(argument list…)

HWTree_CallableBond_OptVal(argument list…)

These functions deal with the valuation of callable bonds. The first values the pure (non-callable) bond with the embedded bond option, while the second returns only the value of the embedded option. The underlying bond may pay a varying coupon rate (e.g. step-up callable) and have a non-level call price schedule. The functions use the following arguments:

 Argument Description Restrictions Valuation_Date valuation date (e.g. today) valid Excel date number Settlement_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) 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 Call_Prices array of call prices per \$100 par corresponding to Coupon_Dates array > 0 if callable on a date = 0 if not callable on a date Notice_Days minimum notice, in days, required to call the bond >= 0 Call_Cost cost per \$100 par to call the bond (issuer cost, e.g. transaction fees) >= 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 Tree_Steps_per_Coupon tree steps per fixed coupon period in the trinomial lattice > 0 (typically 3 to 10)

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