Debenture Pricing Manual
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DEBENTURE PRICING MANUAL 31/03/2020 PUBLIC INFORMATION INFORMAÇÃO PÚBLICA – PUBLIC INFORMATION Debenture Pricing Manual CONTENT INTRODUCTION ................................................................................................ 3 1 GLOSSARY OF VARIABLES ...................................................................... 4 2 PRICING MODELS FOR FIXED INCOME CONTRACTS ............................ 7 3 PRICED DEBENTURES ............................................................................. 10 4 PROCEDURES ADOPTED DUE TO CHANGE IN DEBENTURE CHARACTERISTICS .................................................................................. 12 ANNEX – METHODOLOGIES ......................................................................... 14 1 DEBENTURES SPREAD CURVE .............................................................. 14 2 SYSTEMATIC BIAS CORRECTION MODEL FOR TRADED DEBENTURES ........................................................................................... 22 CHANGE LOG ................................................................................................. 23 2 PUBLIC INFORMATION Debenture Pricing Manual INTRODUCTION This manual presents the calculation methodologies used to generate debentures reference prices and rates disclosed by B3 in the Private Fixed Income segment. Also listed are the characteristics that must be observed in a given bond for it to be eligible for pricing by one of the methods set forth herein. Section 1 defines the variables used in pricing models. Section 2 presents the pricing model for the categories in which the debentures are grouped. Section 3 provides the economic and financial indices covered by the pricing models and the exceptions. Lastly, section 4 describes the procedures adopted due to changes in debenture characteristics. The Annex shows the methodologies for calculating the parameters used for pricing. The calculations presented throughout this document are performed without applying any truncation or rounding. Only the end product of the calculation, the one sent to users, is rounded to the sixth decimal place. 3 PUBLIC INFORMATION Debenture Pricing Manual 1 GLOSSARY OF VARIABLES Debentures contracts are divided into four groups: (i) Fixed Rate, (ii) Floating Rate with Percentage Spread, (iii) Floating Rate with Multiplicative Spread and (iv) Indexed. The methodology used to calculate the reference price and rate is specific to each group. However, the variables and concepts are common to all. This section presents a glossary of the variables used in fixed income contract pricing methodologies and their descriptions. 풕 Mark-to-market date. 풕−ퟏ Business day prior to mark-to-market date. 풕ퟎ Bond yield start date. 푨푴푻%(풆풊) Par Value percentage to be paid on payment flow dates (풆풊). %푰풏풄(풆풊) Percentage of the future value of the i-th interest rate flow to be incorporated into the issuance par value (VNE). 풆풊 Payment flow dates, 0 ≤ ≤ 푛; dates on which the issuer must pay the investor. In the notation used in this document, 푒푖 is the i-th payment flow date; 푒0 is assumed to be the bond yield start date (푡0) and 푒푛 is the last payment date. The set of all these dates will be named 퐸 and the subset will be named 퐸푡, where 푒푖 ≥ 푡. 푵풕 Value in points on the 풕 calculation date of the index correcting the bond issuance par value. 푵풕ퟎ Value in points on the 풕ퟎ bond calculation start date of the index correcting the bond issuance par value. 풓풆풊 Interest rate expressed in % per annum (p.a.) that pays the 푒푖 interest rate event. All rates contained in the models presented are expressed in % p.a., on the basis of 252 4 PUBLIC INFORMATION Debenture Pricing Manual business days (d.u.) capitalized under the compound interest regime. If the interest rates of any bond differ from those mentioned above, they shall be converted to an equivalent rate so that the calculations made are coincident with the characteristics of the bond’s issuance. 푽푵푬 Bond issuance par value. 푽푵푹 Remaining par value, i.e., the amount of the issuance par value that the issuer still owes the investor, minus amortizations already made. 푉푁푅(푡) = (푉푁퐸 + ∑ 푭(풆풌) ∗ (1 − %퐼푛푐(푒푘)) − ∑ 퐴푀푇(푒푘) 푒푘:푒푘∈피푡 푒푘:푒푘≤푡 푻푼 Single contract discount rate obtained through the bisection method. The variables below are defined only in 퐸푡, that is, in payment flows that occur on dates where 푒푖 ≥ 푡. 푨푴푻(풆풊) Amortization Cash Value. In the event of amortization on the issuance par value: 퐴푀푇(푒푖) = 푉푁퐸 + ∑ 푭(풆풊) ∗ (1 − %퐼푛푐(푒푖))) ⋅ 퐴푀푇%(푒푖) 푒푘:푒푘∈피푡 In the event of amortization on the remaining par value: 퐴푀푇(푒푖) = 푉푁푅 + ∑ 푭(풆풊) ∗ (1 − %퐼푛푐(푒푖))) ⋅ 퐴푀푇%(푒푖) 푒푘:푒푘∈피푡 푫푼(풆풊) Business days count between 푡 and 푒푖. 푫푼푪풖풑풐풎(풆풊) Business days count between 푒푖−1 and 푒푖 Payment Flows. 5 PUBLIC INFORMATION Debenture Pricing Manual 푫풖풓(풕) Fixed income contract duration. ∑푒 :푒 ∈피 퐷푈(푒푘) ⋅ 푃(푒푘) 1 퐷푢푟(푡) = 푘 푘 푡 ⋅ 푃푈 252 푭(풆풊) Cash value of the interest rate event to be paid on the 푒푖 date. 푰(풕) Premiums released and not paid by the issuer. 풑 Percentage premium, which may be a premium or a discount, applied to the debenture credit spread. The premium is differentiated by debenture and allows incorporating other factors into the price other than the credit profile. 푷(풆풊) Present value related to the total to be paid at the 퐹(푒푖) flow. 푷푼(풕) Present value of contract, reference price (PU = Unit Price). 푃푈(푡) = 퐼(푡) + ∑ 푃(푒푘) 푒푘:푒푘∈피푡 푹(풆풊) Discount interest rate for the 푒푖 maturity calculated through exponential interpolation. This rate depends on the contract index and will be detailed in the following sections. 푺(풆풊) Credit spread for the 푒푖 maturity calculated through exponential interpolation. The spread is obtained from the credit spread curves for the debenture credit profile. Each fixed income contract is assigned a credit profile and used to obtain the corresponding credit spread curve. The characteristics and payment flows of the debentures used in pricing are those defined in the public issuance deeds of debentures and are reflected in B3's securities registration system. 6 PUBLIC INFORMATION Debenture Pricing Manual Below, we present the calculation specificities of different debenture groups, using the notation presented herein. 2 PRICING MODELS FOR FIXED INCOME CONTRACTS The reference price for liquid debentures, i.e., those that have a minimum trading frequency over a time window, is the average day's trading prices that meet the maximum dispersion criterion weighted by quantity. For other debentures, the price is determined via the models described below. The types of fixed income contracts differ depending on the financial index used for indexation, which is reflected in the methodology used for pricing the bond. Fixed income contracts are classified as fixed rate, floating rate (percentage or multiplicative spread) and indexed. The following are formulas for pricing bonds. 2.1 Fixed rate contracts Are contracts characterized for having their interest rate (푟) and yield known upon issuance. 퐷푈퐶푢푝표푚(푒 )⁄252 ( ) 푎푐푐퐹 푒푖 = (1 + 푟푒) − 1 퐹(푒푖) = 푉푁푅(푒푖−1) ∗ 푎푐푐퐹(푒푖) 퐹(푒푖) ∗ (1 − %퐼푛푐(푒푖)) + 퐴푀푇(푒푖) 푃(푒푖) = 퐷푈(푒)⁄252 [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 퐷푈(푒)⁄252 퐷푈(푒)⁄252 [(1 + 푇푈)] = [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 7 PUBLIC INFORMATION Debenture Pricing Manual 2.2 Floating rate contracts Their indexation is based on an index (퐼푛푑푐(푡)) with an annualized rate on a compound interest basis of 252 business days, such as the CDI (Interbank Certificate of Deposits), which is used for most contracts. Floating rate contracts may be of two types: percentage spread and multiplicative spread. 2.2.1 Floating rate contracts with percentage spread Percentage spread contracts are traded as a percentage (휙푒) of the index interest rate defined at the issuance of the contract. If 푒푖 is the first event immediately following the 푡 mark-to-market date, then: 퐷푈(푡,푒 ) 1⁄ ( ) ( ) 252 푎푐푐퐹 푒푖 = 푓푎푡표푟퐼푛푑푐 ∗ {[(1 + 푅 푒푖 ) − 1] ∗ 휙푒 + 1} 푡 1 ( ) ⁄252 푓푎푡표푟퐼푛푑푐 = ∏ [ 1 + 퐼푛푑푐푘 − 1] ∗ 휙푒 + 1 푘=푒−1 Otherwise: 퐷푈(푒 ) 1 ( ) ( ) 252 푎푐푐퐹 푒푖 = [1 + (((1 + 푅 푒푖 ) ) − 1) ∗ 휙푒] 푎푐푐퐹(푒푖) 퐹(푒푖) = 푉푁푅(푒푖−1) ∗ [ − 1] 푎푐푐퐹(푒푖−1) 퐹(푒푖) ∗ (1 − %퐼푛푐(푒푖)) + 퐴푀푇(푒푖) 푃(푒푖) = 퐷푈(푒)⁄252 [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 퐷푈 1 252 [[(1 + 푅(푒푖)) − 1] ∗ (1 + 푇푈)] 퐷푈(푒)⁄252 = [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 8 PUBLIC INFORMATION Debenture Pricing Manual 2.2.2 Floating rate contracts with multiplicative spread Flow payments of floating rate contracts with multiplicative spread consider the composition of the contract coupon rate (r) with the index interest rate for the calculation of the contract’s yield. Cash flow discount considers the composition of the market credit spread for the contract and the discount rate (푅(푒푖)) for the index (퐼푛푑푐). If 푒푖 is the first event immediately following the 푡 mark-to-market date, then: 퐷푈(푡,푒) 퐷푈(푒) ( ) ( ) 252 252 푎푐푐퐹 푒푖 = 푓푎푡표푟퐼푛푑푐 ∗ (1 + 푅 푒푖 ) ∗ (1 + 푟푒) 푡 1⁄ 푓푎푡표푟퐼푛푑푐 = ∏ (1 + 퐼푛푑푐푘) 252 푘=푒−1 Otherwise: 퐷푈(푒) ( ) ( ) 252 푎푐푐퐹 푒푖 = [(1 + 푅 푒푖 )(1 + 푟푒)] 푎푐푐퐹(푒푖) 퐹(푒푖) = 푉푁푅(푒푖−1) ∗ [ − 1] 푎푐푐퐹(푒푖−1) 퐹(푒푖) ∗ (1 − %%퐼푛푐(푒푖)) + 퐴푀푇(푒푖) 푃(푒푖) = 퐷푈(푒)⁄252 [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 퐷푈 퐷푈(푒 )⁄252 252 [(1 + 푅(푒푖)) ∗ (1 + 푇푈)] = [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 2.3 Indexed contracts Indexed bonds update their issuance par value (VNE) according to the variation of a given 푵 index, which is defined at the contract’s issuance, such as the IGP- M (General Market Price Index) or the IPCA (Extended Consumer Price Index). 9 PUBLIC INFORMATION Debenture Pricing Manual The contract coupon interest rate (푟푒) is then applied over the updated par value to determine the event’s cash value to be paid by the issuer. 퐷푈퐶푢푝표푚(푒 )⁄252 ( ) 푎푐푐퐹 푒푖 = (1 + 푟푒) − 1 푁푡 퐹(푒푖) = 푉푁푅(푒푖−1) ∗∗ ∗ 푎푐푐퐹(푒푖) 푁푡0 푁푡 퐹(푒푖) ∗ (1 − %%퐼푛푐(푒푖) + 퐴푀푇(푒푖) ∗ 푁푡0 푃(푒푖) = 퐷푈(푒)⁄252 [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 퐷푈(푒)⁄252 퐷푈(푒)⁄252 [(1 + 푇푈)] = [(1 + 푅(푒푖)) ∗ (1 + 푆(푒푖)) ∗ (1 + 푝)] 3 PRICED DEBENTURES Public issuances performed through the Brazilian Securities & Exchange Commission (CVM) Normative Instructions No.