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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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### 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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### 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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### Proving that YTM > Current Yield on Discount Bond

I’m currently stuck in proving that for a discount bond: YTM > current yield, with: $$\text{current yield} = c \frac{100}{P}$$ with $P=100-d$ the price of the discounted bond and $c$ the coupon rate....
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### 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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### 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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### 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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### 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 ...
553 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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?
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### Role of the evaluation date ( ql.Settings.instance().evaluationDate )

I have questions about the evaluation date. (set up with ql.Settings.instance().evaluationDate). I'm trying to build the zero-coupon curve from deposit rates and swap rates, however I don't ...
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### 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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### 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 ...