# Tag Info

Accepted

### Do we use the Nelson-Siegel model to calculate the yield curve?

In the beginning, we had a plot of yields of individual bonds against time to maturity, the crudest form of "yield curve." Years later, people began hand-drawing a smoothed line through these yields ...

### Is trading mean reversion of small principal components of prices profitable?

Within the fixed income space, there's a lot of literature on PCA trading. The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement....

### How to de-seasonalize natural gas term structure data?

As a starting point to this, determining seasonality for a given market is as follows: i) Take several years of historical spot price time series, e.g. TTF spot prices. For year $i$ work out a yearly ...
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### SVI model and Greeks calculation

The SVI is simply a function (empirically fit to the data) which given a maturity and a strike price K, computes a BS implied volatility $\sigma$. Once you have that implied volatility you can plug it ...

### What is the state of the art govie bond term structure recently

I interpret your question to be asking about curve fitting techniques (for constructing fitted par/zero curves), since a term structure model (HW, LMM, etc.) can always be constructed to fit a given ...
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### What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

In my understanding, the mortgage prepayment option, at any point in time, is a function of the value of the mortgage from that point in time forward. This value, in turn, is a function of the future ...

### Contango and backwardation in VIX futures

Since contracts on physical goods have associated costs, it makes sense that the term structure curve would be upward sloping. Since there is no cost associated with delivery for the VIX and contango ...
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### Fitting the Term structure of Discount Bonds with Ho-Lee

What they are referring to is a very simplified version of the Ho-Lee model, i.e. on that assumes $$r(t)=r(0)+{\sigma}W(t)$$ where ${\sigma}$ is a constant (annualized StDev). For the sake of ...
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### Deriving interest rate term structure in a short rate model

This is indeed a standard result. You can convince yourself by noticing The bank account grows from 1 at $t=\tau$ to $E\left[\exp(\int_\tau^T r(u)du)|\mathscr{F}_\tau\right]$ at time $T$ The price of ...
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### Valuing derivatives under stochastic interest rates

A few points can be noted. The CIR model is usually for a short, or instantaneous, spot rate $r_t$, which is the forward rate over an infinitesimal interval. That is, \begin{align*} r_t = \lim_{\...

### VXV vs. VIX futures: arbitrage opportunities?

VXV is a 3-month volatility index, and is currently not tradable (there are no futures on it). And since you cannot trade it, you cannot arb it.

### Why should future short rates tend towards the current term structure of interest rates?

It really depends for what purpose you are using the model. Let’s say you are using it for valuation of some instrument. If you want the fair market value, then a) is irrelevant and you would instead ...
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### Applying interest rate models for volaility rate

Hans Buehler investigated this in some detail, including in his doctoral thesis. When I tried it out some years ago, back when volatility exotics were more liquid, I found the models nearly ...

### How to check that an interest rate curve is arbitrage free

To say a curve is arbitrage-free, you need to pick an arbitrage path; a series of trades which, when followed, yield a net profit without creating exposure. We neglect counterparty exposure here, ...
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### Bond Convexity and Maturity

You can understand convexity by working out a simple example numerically yourself. Consider two bond portfolios: P1= consists of a 6 year zero coupon bond. P2= half in a 2 year ZCB, half in a 10 year ...
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### Bond Convexity and Maturity

Think of a zero coupon bond - the pv_zero (t years) $= \frac{\rm{pmt}}{(1+r)^t}$ As t increases the compounding effect of that discount increases (the larger the price change) As for rate vol - ...

### Term structure used in Geometric Brownian Motions under Risk Neutral Measure?

It should be time dependent and set to the spot forward rate $= -\frac{\partial}{\partial t} \ln(\text{discount}(t))$ when simulating in continuous time. When discretizing the simulation use the ...

### Forward interest rate curve family parametrization

You've correctly identified that the forward curve indeed has two time indices -- one for when we observe it, and one for the future date at which the forward rate applies. I would personally take the ...
1 vote

### Hazard rate and Term structure model

The paper on Jun Pan's page. The only quotes readily observable in the market are quotes for a few tenors of the standard CDS contract. Please recall that the standard credit default swap essentially ...
1 vote

### backtest VIX term structure strategy

This is not an answer, but instead advice: Since you're new to quant and volatility then you should start with something other than a volatility or a rates product because those are going to be some ...

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