# Tagged Questions

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### Modified or Macauley Duration in python

are there any existing python modules that can calculate Modified and/or Macauley Duration of a bond.
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### ZSpread in multiple curve framework

how do I calculate ZSpread for a govt. bond in a multiple curve framework? I have not come across the exact details anywhere so I want to verify if I'm right. Below is my understanding, please correct ...
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### How to price an European call on zero-coupon from the yield curve?

It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by $$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$ where ...
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### Help with integrating stochastic calculus expression from yield curve model

I am very rusty on stochastic calculus, and I am having trouble integrating the following simple term from a yield curve model: $$z(t)=\int_0^t\exp(-k(t-s))dW(s)$$ Any suggestions appreciated.
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### How to prove following order?

Consider a consol bond, i.e. a bond which will forever pay one unit of cash at $t = 1, 2, . . ..$ Suppose that the market yield $y$ is constant for all maturities. (a) Compute the price, at $t = 0$, ...
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### I want to Derive $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$

Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond. ...
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### I want to prove Determine the coupon rate $r$, such that the price of the bond, at $T_0$, equals its face value

Consider a coupon bond, starting at $T_{0}$ , with face value $K$, coupon payments at $T_1, . . . , T_n$ and a fixed coupon rate $r$. Determine the coupon rate $r$, such that the price of the bond, at ...
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### In bond pricing, is negative convexity better than positive convexity?

Say that I have two bonds and one of them has positive convexity and the other negative. Which one is better (assuming that you only care about convexity)? I understand that high convexity is ...
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### Provide a bond pricing differential equation and invoke Feynman-Kac

Grateful for any assistance. Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic and $Z=Z(r,t;T)$ is a zero coupon bond. Provide a bond pricing differential equation and invoke ...
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### (Beginer on bond market) References on callable bond's pricing

I am searching for references on pricing callable bonds. I've not find any rigorous mathematical approach on the web. All I found was some soft approaches in a discrete framework. Edit: First of ...
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### Duration calculation for perpetuity with continuous compounding

Let's say we have a continuously compounded perpetuity. Does macaulay duration = modified duration? I've read from wikipedia for Bond Duration that macaulay duration = modified duration for ...
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### Bond Interest Rate Swap Growth Rate [closed]

this should not be here because it shouldn't be here forever and eve
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### Interest rate on loan for purchasing Sterling bond

I am struggling trying to find out where they get the $8$% interest rate for the loan you make to purchase the Sterling Bond in the following strategy: Problem: Suppose that $A(0)$ = $100$ and ...
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### How is USGG10Y (or any tenor) constructed?

I was wondering how the yield curve for US treasuries are constructed (ex. USGG10Y, USGG5Y, etc.). How to compute for it exactly (what deals/quotes are included in it, what financial institutions are ...
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### Why is the duration of a bond important?

I know what duration measures, but now in the age of computers why is it useful? If the yield changes, we could just simply plug the new yield into a program, or excel or something like that, and ...
98 views

### Pricing a bond contract from the yield curve

When giving a particular class in financial mathematics for a student I saw a problem in a list of exercises that says: How to calculate the price at 15 December 2010 of a bond paying a coupon of ...
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### Conversion factor for bonds

Hull defines the conversion factor for a bond as the "quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the interest rate for all ...
144 views

### Cost of Carry Bear Flattener

I was reading a report last week that “the carry on a 2s5s gilt curve flattener is negative to the tune of 10bp over 6 months” and I realised I have little understanding of this concept and ...
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### How are bond prices quoted in the financial press related to bond yields quoted?

For example in the FT this month a 10 year US bond with redemption date 05/24, coupon 2.50 has a bid price of 99.52 and a bid yield of 2.56. Can one calculate the bid yield from the bid price, red ...
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### Concise way of learning Bond & IR models

What is the most concise way to learn about bond and interest rate models from the book Mathematical Models of Financial Derivatives by Yue-Kuen Kwok? I have studied Oksendals Stochastic Differential ...
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### Bond Portfolio Immunization - Duration Matching

**Question is at the bottom** Suppose you have a portfolio of bonds A, B, and C with the following characteristics: (the "Frequency" column is the # of coupon pmts per year and also the # of ...
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### What happens when bond price is less than the recovery rate

I am simulating various price path of bonds, and one issue that came up is the recovery rate. When a bond defaults, the amount you get back recovery rate * principle. This creates a problem if the ...
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### How to benchmark bonds?

I am trying to find for each european bond in my database a proper Benchmark to compare them with the Bloomberg benchmarks for bonds. What i have done so far is to extract a list of all government ...
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### What is the intuition behind the fact that Modified duration = Macaulay Duration / (1+r)?

I understand the derivation of both:take dP/dR and divide by P which will give you both 1) modified duration OR 2) macaulay duration / (1+r) (notice the weighted average time built into the ...
264 views

### Forward rates formulae

I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates. $$\frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)}$$ I can understand the ...
289 views

### Pricing a FixedRateBond in Quantlib: yield vs TermStructure

I am trying to price a simple U.S. treasury in QuantLib, using two methods. The first method calls FixedRatebond.dirtyPrice(...), passing in a YTM and other parameters. The second method involves ...
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### Price change of a bond towards yield and YTM

I have been trying to get a good picture of PV01 and DV01(PVBP). I was going through below link. This measure is the absolute value of the change in price of a bond for a one basis point change in ...
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### Implied Correlation using market quotes

Is there a way to retrieve the implied correlation between stock price and zero coupon bonds?
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### What is the hedging underlying of MBS

I am working on hedging agency MBSs using treasury bonds. So my question raise as which treasury bond should more likely be a hedging underlying of a MBS. What is the matching criteria usually for MBS ...
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### Bond pricing with HJM simulation

I'm using Glasserman 3.16 and 3.17 algorithm to price bonds. The algorithms evaluates the forward rates and the discount factor $B(0,t_j)$. My question is: How can I price bonds in a future time? I ...
740 views

### Calculating instantaneous forward rate from zero-coupon yield curve

I have a big dataset containing zero-coupon bond yields with different relative maturities. I fix a time horizon on my dataset and I want to calculate instantaneous forward rate. I'm going to write ...
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### If we modify duration, should we modify bond price? Options Futures and Other Derivatives

In Example 4.5 of Section 4.8 on Duration of Options, Futures and Other Derivatives (p.92), a bond's price and duration are computed assuming continuous compounding where the bond yield is y = 12%. ...
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### Can the duration of a bond be greater than Time to Maturity

In the case of a vanilla bond I know that the duration will be less than the time to maturity. But I am observing that for a non-vanilla bond, the duration is greater than time to maturity. Can ...
298 views

### Interpolating spot rates given intermittent coupon-bond prices.

I'm trying to bootstrap spot rates given coupon-paying bond data. To simplify my problem, assume we are working with only 3 given data, the price/coupon rate on semi-annual bonds maturing in 0.5, 1, ...
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### How to determine risk-free rate of Ecuador?

I have a question in determining the risk-free rate of Ecuador. For developed countries like United States and Great Britain, the risk-free rate can be obtained in financial database such as Reuter or ...
141 views

### Arbitrage with freshly issued bonds

I recently heard someone mention an arbitrage strategy involving selling freshly issued bonds and buying the "old batch" as it has shown that the liquidity in the fresh batch motivates/drives up these ...
151 views

### Given monthly returns of 10-Year Govt Bond, how to get monthly risk free rate of return

I have a list of monthly returns of a 10 year Govt Bond. I am not sure if this is a good proxy for the monthly risk free rate of return. Can somebody suggest how I can derive the monthly risk free ...
229 views

### Pricing credit risky bonds

How do we price credit risky bonds? If I discount the cash flows using LIBOR/zero rates, it won't take the credit riskiness into account. So should I use a rate based on the issuer's credit spread? ...
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### Get discount factors with limited knowledge?

I am facing the problem of just having this information: 6% coupon bond with 2.5 years to maturity, traded at a 100% clean price 4% coupon bond with 1.5 years to maturity, traded at a 98% clean price ...
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### Definition of gearings, spreads and curve in RQuantLib's Floating Rate Bond function

Consider the RQuantLib package function FloatingRateBond(). This takes as inputs gearings ...
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### Does YTM represent interest? [closed]

Does a bond's Yield to Maturity represent the amount of interest one gets at maturity even though it's expressed as a percentage? I read that it is a rate of return on a bond at maturity, but what is ...
700 views

### RQuantLib, Hoadley and Bloomberg YAS: fixed rate bond pricing differences?

I'm trying to price a fixed rate bond one year from now on. The bond is the PEUGOT 7 ⅜ 03/06/18, whose ISIN code is FR0011439975. I'm using such a specific example because in this way everyone can ...
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### RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?

Please, consider the following functions from RQuantLib package: FixedRateBond() ...