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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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Are pure PIK bonds' payoffs known from the start?

I am developer working in the financial field and I would like to understand what I'm doing. My latest work subject involves Payment In Kind bonds with coupons fully reinvested (e.g, no coupons ...
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2answers
1k 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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1answer
61 views

Ho-Lee short rate model under the Heath-Jarrow-Morton framework

Under the Heath-Jarrow-Morton (HJM) framework the dynamics of the Ho-Lee short rate model are defined as following: $$dr(t)=\theta(t)dt+\sigma dW^{\mathbb{Q}}(t)$$ with $\mathbb{Q}$ the risk-neutral ...
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1answer
95 views

stress testing zero coupon yield curve

i'm currently trying to stress test the zero coupon yield curve using daily observations from 2003 to 2019. Each Zero coupon yield curve originate from an actuarial curve with 37 tenors that range ...
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3answers
555 views

Basic boostrapping question

Suppose I have three bonds: Coupon bonds are paid semi-annually. Rates are continuous compounding. I'm trying to bootstrap the zero rates for 0.5 years maturity using the 1 year zero coupon bond and ...
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0answers
67 views

Zero Coupon Volatility data

I am trying to construct a Black-Derman-Toy trinomial tree as explained in Espen Haug's Complete Guide to Option Pricing Formulas, chapter 11. Where do I get the Inputs (table 11-2) from if I wanted ...
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44 views

Risk mapping a zero-coupon bond portfolio

I'm trying to understand example 2.6 taken from McNeil and Embrechts "Quantitative Risk Management". The example consists of obtaining the risk mapping of a portfolio of $d$ zero-coupon bonds. The ...
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1answer
121 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 ...
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2answers
76 views

Why do constant maturity bonds account for modified duration?

One can create a constant maturity treasury (CMT) by building a zero coupon discount curve and generating constant maturity bonds from that curve. This allows one to look further back than is possible ...
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1answer
99 views

a property of zero coupon bond in Brigo/Mercurio's “Interest Rate Models”

Let $P(t,T)$ be the the value of a contract at time $t$. This contract guarantees its holder the payment of $1$ at time $T$. consider $t<T<S$, when the interest rate is non-deterministic, do ...
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1answer
374 views

Pricing the discount zero-coupon bond under a jump-diffusion model

I am going to get the price of a zero coupon bond in a jump-diffusion model. The dynamic of interest rate as follow $$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,...
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1answer
40 views

When estimating P/L through greeks based on zero rate curves, does it contain time (theta) PNL?

Suppose on day 1 we calculate a delta wrt. a point on an interest curve of zero rates, we then let 1 day pass, recalculate the interest curve of zero rates with the same bonds (though now day 20 bond ...
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1answer
117 views

EURIBOR zero rates vs forward rates to project future income on a bank's loans

I work at an international bank within the M&A FIG team, and have seen that my associate uses the future daily EURIBOR 3M,6M,12M to estimate what the future interest income on a banks loans will ...
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0answers
39 views

Using above par zero coupon bond to build a zero coupon curve

Should I discard bonds above par (zero coupon bond with market price over par value) when I build a zero coupon curve? Most of the academic textbooks use bonds below par as inputs to build Zero ...
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1answer
88 views

Zero Coupon Curve and Floating Rates Notes pricing

Simple question: Can I use a Zero Coupon Curve (using Treasury or Swap Curve) to price floating rates notes (FRN)? I am building a classic Zero Coupon Curve, however I wonder if I can use it to ...
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2answers
771 views

How to show that the exponential Vasicek model is not an affine term-structure model?

From the pricing formula, we know that the value at time $t\in [0,T]$ of a zero coupon bond maturing at time $T$ is $$ B(t,T)=E\left(\exp{\left(-\int_{t}^{T}r_sds\right)}\bigg|\mathcal{F}_t\right). $$...
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1answer
221 views

Swiss Zero-Coupon Bond Yield Curve Data

I am trying to access the Swiss Zero-Coupon Yield Curve Data. I know that the Swiss National Bank provides this data, as noted on the 8th Page of this paper under Section 3.2. However, I am for the ...
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1answer
124 views

Difference between ED futures and ZCB

I am new to rates and learning the basic products. It seems to me that Eurodollar contracts are similar to zero coupon bonds except that it locks in the interest. So I want to clarify if I am ...
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1answer
71 views

yield concept for a short maturity zero coupon bond

I am trying to clarify what is the more relevant and appropriate quantity for a discount security / zero-coupon bond, that is defined by a face value, FV, a present value, PV and a time to maturity, t,...
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1answer
810 views

What is the delta of a zero coupon bond? [closed]

I understand that zero coupon bond changes as interest rates change. But I am unsure of how to get the delta. Say I buy a 5Y zero coupon bond with notional amount 5M USD. How do I calculate the delta? ...
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2answers
2k views

Zero rate curve USD Libor

Good day, I gave following inputs of Libor rates : ON 0.3731 1W 0.3939 1M 0.4265 2M 0.5148 3M 0.6176 6M 0.8655 1Y 1.1336 How can I build zero-rate curve ?
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2answers
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How are zero-coupon bonds issued?

I am thinking of the cashflows structure of zero-coupon bonds. I am wondering whether they are usually issued below par or at par. It's more natural for me thinking that they are priced below par, but ...
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1answer
502 views

Pricing zero coupon bonds on a yield curve

I'm getting confused about how I should price the current price of a zero coupon bond when there are several yields to choose from. For instance, lets say that there is an upward sloping yield curve. ...
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0answers
147 views

Zero coupon bonds dynamics

The dynamics of a zero coupon bond under the risk neutral probability are: $$\frac{dP(t,T)}{P(t,T)}=rdt+\sigma(t,T) dW_t$$ What happens if I take the limit for the maturity $T$ going to small $t$? Do ...
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1answer
496 views

zero coupon bond pricing formula using Hull White

I am having some trouble to understand the derivation of the parameters of zero coupon pricing formula using Hull White. Specifically I am trying to understand how to get --[1] where is the ...
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506 views

Duration of callable zero coupon bond

Can anybody please help me out with the below question with a brief explanation:- A 10-year zero coupon bond is callable annually at par (its face value) starting at the beginning of year 6. Assume a ...
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1answer
133 views

Zero-coupon Loan Investment [closed]

Zero-coupon default-free interest rates maturing over the next five years are listed below (in percent per annum, continuously-compounded): Maturity Years -- Yield 1 --------------------1.9 2 ------...
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1answer
574 views

Zero Coupon Bond Forward Price

I'm currently working on the Coursera Financial Engineering and Risk Management course. In one of the questions I was asked to build a binomial pricing model for fixed-income securities. Specifically ...
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1answer
513 views

What techniques can be used to get the missing maturities from the CMT yields?

I have constant maturity treasury data from the h15 release of the FED, from which I use 6 month, 1 year, 2, 3, 5, 7, 10, and 20 year yields. I want to strip the zero coupon curve, but am not sure ...
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1answer
171 views

example regarding zero coupon bonds

This example is from Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by Carmona, René, Tehranchi, M R. I am wondering if the calculation is correct?, he says ...
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2answers
80 views

Can we derive 5 year zero coupon interest rate by using 1, 2 and 3 year zero coupon interest rate?

Given that the 1 year zero coupon bond interest rate is 5%, 2 year zero coupon bond interest rate is 6% and 3 year zero coupon bond interest rate is 7%. 4 year coupon bond price and interest rate are ...
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1answer
153 views

Coupon bond pricing problem with reinvestment

The three year bond has face value USD 100, and pays USD 5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%. (a) Find the price of this bond. (b) ...
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2answers
82 views

zero coupon problem calculus

I encounter a problem: do we have the following equality : $B(0,T_{i})e^{\int_{0}^{t}r_{s}ds}=B(t,T_{i})$ and if yes why because I am stuck with this ... I try to use that : $B(t,T_{i}) = B(0,T_{i})e^...
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1answer
1k views

Zero coupon bond pricing under Extended Hull & White

How do you price zero coupon bond in extended Hull & White model by solving the Bond Pricing Equation??
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826 views

How to price a credit-risky zero-coupon bond?

I recently received the following exercise: Construct a $n=10$-period binomial model for the short-rate, $r_{i,j}$. The lattice parameters are: $r_{0,0}=5\%$, $u=1.1$, $d=0.9$ and;...
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2answers
254 views

Is $\frac{P(t,S)}{P(t,T)}$ martingale?

Assume $r_t$ follow the CIR process and $P(t,T)=E[exp(-\int_{t}^{T}r_s ds)|F_t]$.I am going to show $\frac{P(t,S)}{P(t,T)}$ ($S<T$) is an $F_t$-martingale under Forward Measure but So confused! Do ...
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1answer
117 views

Constructing NS-Svensson parameters with zero coupon AND coupon bonds

I am in the process of calculating sovereign zero coupon yield curves using the NS-Svensson parameter for a number of countries. Due to data constraints, I would like to use the information from price ...
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1answer
153 views

Transforming coupon bond returns to ZC bond returns

I am interested in aggregated Amihud ratios measures over bond groups. For a large panel data set with daily bond prices and volumes I have calculated already Amihud ratios per ISIN/day. Naive ...
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1answer
120 views

Zero rates coupon bond calculation

In order to do cash flow mapping I need zero rates for corporate bonds , where to find or how to find the o rates ?
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Zero rate vs. yield on coupon bearing bond

in Hull's solutions manual of Options, Futures & Derivatives (8th edition), there's question 4.7, in which is asked to put the following in descending order: a) the five-year zero rate, b) the ...