Questions tagged [zero-coupon]

A debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value.

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From Libor Curve rates to "forward" zero-coupons

I am provided a 6M euribor curve, constructed from FRA's and swaps of tenor 6M on the euro, as well an EONIA curve, constructed from zero-coupons EONIA swaps. Both curves are provided as functions $d\...
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1 answer
106 views

Stochastic representation of a zero-coupon bond

In Chapter 9 of Shreve's book Stochastic Calculus for Finance II, the main theorem is the 9.2.1. Defining the discounting process $D(t)=\mathrm{e}^{-\int_0^t du r(u)}$ and $r(u)$ the, possibly ...
2 votes
1 answer
100 views

QuantLib: Pricing BRL zero coupon swap using relevant attributes in Quantlib

I am trying to price the BRL zero coupon swap. As we know that ZC swaps fixed payer pays a single payment at maturity and the float payer pays the interim payments till maturity. So in this case, ...
2 votes
4 answers
774 views

Construct a zero coupon bond

Suppose a 3% 10-year bond is trading at 89 and a 7% 10-year bond is trading at 97. Then (assuming no arbitrage) the price of a 10-year zero-coupon bond would be: The answer should be 83. How using ...
0 votes
1 answer
182 views

QuantLib: How to price or construct a zero coupon swap using Quantlib

I am trying to construct and price the zero coupon swap. However its giving me the AttributeError: module 'Quantlib' has no attribute 'ZeroCouponSwap'. Please let me know how to price the zero coupon ...
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Why are we so focused on Zero Coupon Bonds?

In fixed income markets there seem to be two prevailing term structure modelling approaches: Market Models HJM Framework In Market Models, such as the LIBOR Market Model (LMM) and SABR it is common ...
3 votes
1 answer
134 views

Zero Coupon Bonds for Structured Products

I'd like to find out how to calculate the level of a zero coupon bond that goes into a fully funded structured product. Let's say SocGen or JPM issue a 2Y fully funded structured note (zero coupon + ...
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0 answers
103 views

Zero-coupon bond price in the risk-neutral word

In Hull's technical note (http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote31.pdf), on page 3, in the third row from the bottom, a plus sign suddenly appears before σ dz in an ...
3 votes
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Arbitrage Opportunities in a Two-Zero Coupon Bond Market

Question: Suppose we are in a market where there are only two zero coupon bonds, both with a face value of 100: the first one with a maturity of one year and a price of 90, and the second one with a ...
0 votes
0 answers
281 views

Estimating market price of interest rate risk under CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
2 votes
0 answers
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Filipovic: Where is it used that the world is deterministic

In this text (Damir Filipovic, Term-Structure Models, Springer, 2009) $P(t,T)$ denotes the price of a zero-coupon bond at time $t$ with maturity $T$. I cannot see where the proof uses the ...
2 votes
1 answer
713 views

How does Bloomberg use the OIS curve to get the zero rates?

I'm trying to reproduce the zero rates using the market rates, but I have not been able to. I read the Bloomberg's "Building the Interest Rate Curve" paper and followed the formulas exactly ...
1 vote
0 answers
72 views

From Discount Factor to Zero rate [duplicate]

Hello guys, starting from this picture, which is the method that you usually use in order to find Zero Rate from Discount Factor? Thank you in advance
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2 answers
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Rationale for issuing zero coupon bonds

I have a conceptual question regarding zero-coupon bonds. Say a bond issuer has issued a bond for funding itself, this bond has been split by the issuer (for simplicity assuming issuer is the same as ...
1 vote
1 answer
116 views

Pricing near to expiration bonds using QuantLib

I want to get the theoretical price of a zero coupon bond each day using quantlib, I'm able do to this up to just before the maturity date where I get the following error: ...
1 vote
1 answer
330 views

How to calculate the discount factors for two deposits in an interest rate curve [closed]

I am trying to calculate the zero rate for a piecewise linear zero curve. I have the following deposit on the short end STIBOR 1D, is identified as a tomorrow next deposit: 0.02416 STIBOR 3 Month: 0....
1 vote
1 answer
1k views

discount factor, zero rates, zero curve from BBG

How can I calculate the discount factor for row 1? I would do $$ \frac{1}{(1+ 2.13763/100)^{(90/360)}} = 0.994726197703956 $$ My ultimate goal is to reproduce the Zero Rates. Any hints welcome. ...
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0 answers
192 views

Replicating strategy for the zero-coupon bond in the Hull-White model

I would like to derive a self-financing, replicating strategy for a call option on a zero-coupon bond in the Hull-White model. I tried to use Proposition 21.10 in 1, in which zero-coupon bonds are ...
2 votes
1 answer
204 views

Strange Market Data YTM for a Zero Coupon Bond

I am trying to compute the YTM of the following Zero-Coupon Bond: The issue date was 13-01-2022 and the maturity date was 14-01-2023. For me, it seems strange that the price remains "almost ...
3 votes
3 answers
252 views

Estimate yield of coupon bond given yield of zero coupon bond

Suppose that now is August 2006 and we have the following zero-coupon bonds: Maturity: August 2007, Price: 95,53 ...
2 votes
0 answers
97 views

Path integral approach to price call option on zero coupon bonds

I am given the following identities: $$ Z[J,t_1,t_2]=\int D W e^{\int_{t_1}^{t_2}dtJ(t)W(t)}e^{S}=e^{\frac{1}{2}\int_{t_1}^{t_2}dtJ(t)^2} $$ $$ \int_t^Tdx\alpha(t,x)=\frac{1}{2}\left[\int_t^Tdx\sigma(...
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1 answer
433 views

Monte Carlo price of European option on ZCB under Vasicek short rate

I'm trying to replicate the analytical result from the closed form Vasicek formula for European options on zero-coupon bonds using Monte-Carlo simulation. The interest rate paths I've simulated seem ...
1 vote
1 answer
321 views

Convert UST Yield Curve to Spot Curve (Zero Coupon) using bootstrapping

Having the following UST Active Curve : Tenor Tenor ticker bid_yield Coupon 1M 912796XM Govt 1.891 0 2M 912796XV Govt 2.225 0 3M 912796V6 Govt 2.52 0 6M 912796XS Govt 3.026 0 1Y 912796XQ Govt 3....
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short rate, yield curve and zero-coupon bond price formula under CIR mode: How to calibrate the market price of risk

I recently read a document posted by a user in QF, who said that "In the past, I have calibrated simple short rate models to the term structure by using maximum likelihood to get the parameters ...
1 vote
1 answer
351 views

Does a bond pay a coupon at maturity? [closed]

I know a bond pays an annuity cashflow of coupon payments and then at maturity it pays the face value. But, at maturity, does it pay an additional coupon payment on top of the face value or are we ...
1 vote
2 answers
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How do you construct a zero coupon curve from the current market yield curve?

If I was to take the current market yield to maturity and tenor for all bonds for a particular issuer how can I convert this curve into a zero-coupon curve? For example if we were to get the yield and ...
0 votes
1 answer
286 views

Zero Coupon Bond - Price and Yield when interest rate is a diffusion process and 0 "price of market risk"

Given that the price of market risk (or market price of interest rate risk) is $\lambda(r_t, t)=0$ and that we have the following dynamics of the interest rate (under the physical measure $P$. $$dr_t =...
2 votes
0 answers
156 views

Zero coupon price using Vasiceks model under the Real-world P measure model

I'm wondering if there is a way to work out the formula for the price of the zero-coupon bond using the Vasicek's model (P measure). I have tried to find reference on it but could not, I don't know if ...
1 vote
1 answer
184 views

How to calculate zero-coupon curve for Italian BTPs?

On the BTP curve, we have the following Bonds (just showing you an extract) I want to calculate z-spreads my self therefore I need the zero-coupon curve. How do I go about doing this? Do I look at ...
3 votes
0 answers
104 views

Is this term structure model valid? (Modeling the Zerobonds directly)

Let us define the dynamics of the discounted Zerobonds as $$ \tilde{P}(t,T) = \int \sigma(t,T) dW_t + \tilde{P}(0,T)$$ Lets assume $\sigma(t,T)$ is s.t. $\tilde{P}(t,T) $ is a martingale and positive (...
3 votes
1 answer
283 views

Volatility and drift of the instantaneous forward rate under risk neutral measure using the zero coupon bond

I have question about this problem. I believe I have derived $f(t,T)$ correctly using the zero-coupon bond. But I am unsure about how to go forward with the question and how to use the second part. ...
2 votes
1 answer
157 views

Proof about discounted zero coupon bond

Hey guys I am having trouble finishing this proof: Proposition 5.1 Under the above assumptions, the process $r$ satisfies under $\mathbb{Q}$ $$ d r(t)=\left(b(t)+\sigma(t) \gamma(t)^{\top}\right) d t+\...
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1 answer
1k views

Zero Rates for Deposits using Quantlib Python

I have used QuantLib Python to construct a zero curve from deposits and bonds. Below are my codes: ...
14 votes
2 answers
19k views

What does instantaneous forward mean?

Could you please help me to understand meaning of instantaneous forward rate? I mean economic interpretation at basic level. What is it used for? How can i derive it from zero rate/price? Thanks
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223 views

How to bootstrap zero coupon rates and what is the relationship with par yields

I understand the basic logic of bootstrapping zero coupon rates (take a bond, discount each cashflow at the prevailing/previously solved zero rate, and solve for the last rate at the last cashflow). I ...
6 votes
1 answer
896 views

Martingale measure and replicating portfolio in Risk Neutral Pricing of Defaultable Zero-Coupon Bonds

When pricing a defaultable zero-coupon bond the risk-neutral price is given as the expected value of the discounted payoff of the bond under a risk-neutral measure. My first question is how do we ...
0 votes
0 answers
119 views

Price of european call option for different strike prices

Consider two european put options with strike prices $K, J$ with $K<J$ and maturity $T$. Then the no arbitrage assumption implies $P_{K}(0)<P_J(0)$, where $P_K(0)$ denotes the price of the put ...
1 vote
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How can I find the distribution function of the following random variables?

Suppose that the random variables $Z_i$ are defined as follows: \begin{equation} Z_i = D(0, t_i)(R_{i-1} +c)\Delta N, \end{equation} where $D(0, t_i)= \exp\{-\int_{0}^{t_i} r_u du\}$ for which $r_u$ ...
2 votes
2 answers
2k views

bootstrapping bloomberg

Does anyone know the zero rate here at -0.23022 is derived? I have tried (1+0.0056*0.503)*(1+-0.00232*0.086)=(1+?^(1/0.589). Solving for ? gives me -0.002344. I have tried simple and compounded ...
4 votes
3 answers
613 views

Nelson Siegel Model calculation of the zero bound price at time zero that expires in 2 years

I am somewhat stuck and not sure how to proceed, so any help would be appreciated. I got the Nelson Siegel model with all parameters for the real data. The curve that is produced is yield vs maturity. ...
0 votes
2 answers
169 views

Getting Bond Price Data

I am on my thesis about Hull-White model and I need the bond price to calibrate the parameters. How can I get historical bond price data instead of historical bond yield data?
1 vote
2 answers
347 views

How do I pricing a ZCB using CIR (Cox-Ingersoll-Ross) model

Please see the codes below My question is about input parameters (a, b and sigma)and their calculation. For the long term mean "b", do we use effective Fed Fund rates? or 3m T-bills? Also, ...
0 votes
1 answer
547 views

MonteCarlo Value at Risk for a bonds portfolio

As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds. I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models. Next steps ...
0 votes
1 answer
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Hedging With Zero Coupon Bonds from The Concepts and Practice of Mathematical Finance by Mark Joshi

In section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of how we arrived at $K' = K\frac{1+d}{1+r}$, but I got a little lost when he ...
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2 answers
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Value of a 30 year bond using the Yield curve

If I buy a $1 30 year bond with 4% coupon payment, would my cash flow be: $$ V^{30}(t) = \frac{$1 \times0.04}{1 + R(t, 1)} + \frac{$1 \times0.04}{1 + R(t, 2)} + \cdots + \frac{$1 + $1 \times0.04}{1 + ...
2 votes
2 answers
1k views

Quantlib: convert par swap rates to zero rates back and forth

I built a zero-coupon curve out of a generic par swap rate curve (Step 1) and I am trying to recover the swap curve back from the zero-coupon curve (Step 2). Step 1 works but not Step 2. I get close ...
1 vote
0 answers
928 views

Calibrating Vasicek model for historical data

I need to to estimate the parameters of vasicek model to predict the zero curve. My database has 4k daily observations of zero rate for 37 maturities. My question is do I have to estimate the model ...
1 vote
1 answer
413 views

Risk-Neutral Pricing Formula for Zero-coupon bonds with Default Risk

I am looking for the equations or papers showing the risk-neutral pricing for zero-coupon bonds including default risk. I already tried Googling and searching SSRN and Jstor.
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1 answer
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T-Forward Measure, LMM & the Zero T-bond

the zero-coupon T-bond is widely used in the industry as a tool to derive pricing formulas: for example it is used in the derivation of the Libor Market Model. The way in which it is often used ...
1 vote
1 answer
663 views

Vasicek Model, zero coupon bond question [closed]

I am trying to solve questions in the Vasicek model. Can anyone help me to solve this question... In the Vasicek model with parameters $\theta = 0.08$, $k$ = 2.5, $\sigma = 0.2$, assuming to be ...