Obbligazioni indicizzate inflazione BTPi - Titoli di Stato indicizzati all'inflazione (1 Viewer)

p_dinamite

Forumer attivo
Facendo 2 prove numeriche ho trovato la soluzione:
in effetti l'inflation calcolata come (1+ inflation) = ((1+RF))/((1+RR))

sostituita in caso a cedola RR=3% RF=5% INF= 0.019417475 n=7

3*([(1+t.infl)/(1+TIR.X)]+ [(1+t.infl)/(1+TIR.X)]^2+....+[(1+t.infl)/(1+TIR.X)]^6) +103 [(1+t.infl)/(1+TIR.X)]^7 =100

e anche nel caso RR=2% RF=3.5% INF= 0.0147 n=12

2*([(1+t.infl)/(1+TIR.X)]+ [(1+t.infl)/(1+TIR.X)]^2+....+[(1+t.infl)/(1+TIR.X)]^11) +102 [(1+t.infl)/(1+TIR.X)]^12 =100

si può quindi ritenere correttamente di calcolare l'inflation come rapporto tra 2 tir con scadenza analoga

BEI= ((1+rendimento nominale%) / (1+ rendimento reale%)) -1
 

zitto-ma-dritto

Nuovo forumer
In effetti l'equazione:
BEI= ((1+rendimento nominale%) / (1+ rendimento reale%)) -1
equivale a scrivere:
Rendimento nominale%=rendimento reale%+inflazione%
a meno dell' infinitesimo:
rendimento reale%*inflazione%
 
Yunus80

Yunus80

Del PIG non si butta nulla
Vi confesso che non ci stavo capendo niente, poi per fortuna siete scesi fino alle formule che usiamo di solito noi mortali... :D
Non sono tanto d'accordo con gli infinitesimi però: consideriamo inflazione al 5% (non fuori del mondo) e rendimento reale al 3% (ottenibile un annetto fa coi BTPi), abbiamo un rendimento composto di 1,05*1,03 -1 = 8,15% mentre la somma dei due fa l'8%.
Per cui vale la pena di tenere presente la composizione delle due parti, come peraltro state già facendo :)
 

olomorfo

Nuovo forumer
forse può essere utile quest'articolo
http://www.ecb.int/pub/pdf/scpwps/ecbwp830.pdf

"The most common way to compute BEIRs has been to simply subtract the yield-to-maturity on a specific inflation-linked bond, from the yield-to-maturity R on a specific
nominal bond with comparable maturity (BEIR = R − RIL). However, the estimation
of a term structure of zero-coupon real rates and corresponding BEIRs offers two major
advantages. First, it allows the calculation of time series of real yields and BEIRs with
constant maturity, which is particularly useful when assessing developments over a
relatively long period of time. The maturity of observed yields and rates from existing
bonds, by contrast, is not constant but declines over the existence of the bonds, which
may complicate the interpretation of yield developments. Second, the calculation of
zero-coupon rates allows potential distortions related to the different durations of the
bonds used in the calculation of BEIRs to be avoided. Such distortions are related to
the different cash-flow structures of inflation-linked and nominal bonds.15
3.2 Estimating term structures of real yields and inflation
Constant-maturity zero-coupon BEIRs can be constructed by subtracting zero-coupon
real rates from zero-coupon nominal rates of the same maturity. Hence, the problem
of computing constant-maturity zero-coupon break-even rates reduces to estimating
real and comparable nominal zero-coupon yield..."
 
Ultima modifica:

p_dinamite

Forumer attivo
grazie dell'articolo che mi appresto a leggere con attenzione.

il discorso della formula BEI= ((1+rendimento nominale%) / (1+ rendimento reale%)) -1

funziona perchè i tassi sono tassi interni di rendimento in capitalizzazione composta...
e in effetti gli esempi numerici han funzionato
 
Maino

Maino

Senior Member
olomorfo ha scritto:
forse può essere utile quest'articolo
http://www.ecb.int/pub/pdf/scpwps/ecbwp830.pdf

"The most common way to compute BEIRs has been to simply subtract the yield-to-maturity on a specific inflation-linked bond, from the yield-to-maturity R on a specific
nominal bond with comparable maturity (BEIR = R − RIL). However, the estimation
of a term structure of zero-coupon real rates and corresponding BEIRs offers two major
advantages. First, it allows the calculation of time series of real yields and BEIRs with
constant maturity, which is particularly useful when assessing developments over a
relatively long period of time. The maturity of observed yields and rates from existing
bonds, by contrast, is not constant but declines over the existence of the bonds, which
may complicate the interpretation of yield developments. Second, the calculation of
zero-coupon rates allows potential distortions related to the different durations of the
bonds used in the calculation of BEIRs to be avoided. Such distortions are related to
the different cash-flow structures of inflation-linked and nominal bonds.15
3.2 Estimating term structures of real yields and inflation
Constant-maturity zero-coupon BEIRs can be constructed by subtracting zero-coupon
real rates from zero-coupon nominal rates of the same maturity. Hence, the problem
of computing constant-maturity zero-coupon break-even rates reduces to estimating
real and comparable nominal zero-coupon yield..."
Clicca per allargare...

grazie ler l'articolo, olomorfo, ed un caldo benvenuto al nostro forum che spero diventi anche il tuo :up:

a presto !

maino
 

p_dinamite

Forumer attivo
ottimo intervento, mi sembra che le opinioni di illustri matematici convergano verso il ns. lavoro...
infatti si trova che:" the increase in a particular
forward inflation rate will not impact the BEIR by the same amount as it will affect the
average inflation over the period ending at the bond maturity.
Essentially, this is similar to comparing the impact of an increase in a forward rate on the
ytm of a nominal coupon bond versus the impact on a zero bond ytm with the same
maturity."
 
You must log in or register to reply here.

Users who are viewing this thread

Total: 2 (members: 0, guests: 2)
Alto