# Tagged Questions

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### How can we have negative probabilities in finance? Can we have negative payments in bonds? If not, how else can we have negative probabilities?

In Half of a Coin: Negative Probabilities, the author mentions bond duration. Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is ...
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### Pricing Treasury futures

I've recently learned that at the delivery of Treasury futures the short side can decide which of the $n$ Treasury bonds (with relevant maturities) to deliver. If the short side chooses to deliver the ...
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### Why can CDS indices be used as a bond market index?

I don't understand why the iTraxx indices family, which are credit default swap indices, are in practice often used to gauge the bond market. How are CDS prices related to bonds prices? And what other ...
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### 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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### 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 ...
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### Positive VaR when calculation on Total Return Indexes?

I recently saw a VaR calculation, and I was wondering whether that calculation made sense. Here the details: 1. Construction of a total return bond portfolio index. By total return I mean that the ...
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### Compare the IRRs of two bonds

Say i have two 3 year bonds, which pay an annual coupon of 8% (1st bond) and 10% (2nd bond) respectively. Also, let's assume, that the spot curve is the same for both bonds. Other things equal, how ...
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### Wrong discount factors when finding Nelson Siegel Svensson model parameters

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non- Linear Optimization problem to do this. Some of the code I have written is below and this is where my ...
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### Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
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### Yield of a risky bond

When working with risky bonds, i.e. corporate bonds, what is usually defined as the yield of such a bond? Is it the yield calculated as if the bond was riskless, or is it calculated by properly taking ...
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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 can I interpret US treasury?

I try to understand US treasury in the bond markets provided by bloomberg: In this webpage, I have a few questions, for instance taking 12month-Bill: (1) What is the maturity date? I find that it ...
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### Bond price under Poissonian model of interest rate

Working through an exercise in interest rate modelling and I have the following setup: $r_t = r_0 + \delta N_t$ where $\delta > 0$ and $\lambda > 0$ is the intensity of the Poisson pricess $N_t$...
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### 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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### Calculating IR sensitivity

I'm trying to figure out how to find IR sensitivity of a bond whose time to maturity of a bond is 2 years. Bond pays 10.875 percent coupons yearly. Duration is 1.8 years. How do you find the ...
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### Why is my YTM incorrect? How does accrued interest play into Yield to Maturity?

I'm writing some software that includes a feature to calculate Yield to Maturity for a Bond. I'm using an HP 10bii Financial Calculator to double check the answers produced by my software. I'm running ...
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### $\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$

How can I show that payment of $\frac{1}{p(T_{i-1},T_i)}(A-p(T_{i-1},T_i))^+$ at time $T_i$ is equivalent to a payment of $(A-p(T_{i-1},T_i))^+$ at time $T_{i-1}$ ? Where A is a deterministic constant....