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10 votes
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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 ...
Helin's user avatar
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5 votes

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 ...
ZRH's user avatar
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5 votes
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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 ...
Alex C's user avatar
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5 votes
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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 ...
Kermittfrog's user avatar
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5 votes

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 ...
Helin's user avatar
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3 votes

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 ...
amdopt's user avatar
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3 votes
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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 ...
g g's user avatar
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3 votes
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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_{\...
Gordon's user avatar
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3 votes

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.
onlyvix.blogspot.com's user avatar
3 votes
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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 ...
rbm's user avatar
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3 votes

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 ...
dm63's user avatar
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2 votes

What is drift in interest rate term structure model

Many term structure models-both single-factor and multifactor imply dynamics for the short-term riskless rate $r$ that can be nested within the following stochastic differential equation: $dr = (\...
phdstudent's user avatar
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2 votes
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How to show that the exponential Vasicek model is not an affine term-structure model?

Here is a general proof for all parameters in an open domain. $$dr = adt+bdW:=r\big(k(\theta-x)+\frac12\sigma^2\big)dt+\sigma rdW.$$ Let $$u(r(s),s):=e^{-\int_t^sr}B(r(s),s,T)=:\phi(s) B.$$ Then $$u(...
Hans's user avatar
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2 votes

How to apply PD term structure?

By the looks of it your table is cumulative PD. You can use the argument: $$P(\text{Default by end year X}) = P(\text{Def. by end year X-1}) + P(\text{Not def. by end year X-1})P(\text{Def. in year ...
Attack68's user avatar
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2 votes

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 ...
Alex C's user avatar
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2 votes
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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 - ...
cifc's user avatar
  • 36
2 votes

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 ...
Antoine Conze's user avatar
2 votes

Why do increasing spot rates have to be equal to or larger than the corresponding par rates?

To answer this question, we must fix a bit of the vocabulary, first. I will try to stick as close as possible to your conventions: Spot rate: (also called zero rate) is the annualised rate of return ...
Kermittfrog's user avatar
  • 6,628
2 votes

What is "implied skew" and "spot/vol beta"?

For what date is the chart derived? One definition for implied volatility skew is: (25 delta put implied volatility - 25 delta call implied volatility) / 50 delta. Can you test to see if this ...
AlRacoon's user avatar
  • 6,532
2 votes

OIS rate to build Term structure

By definition, the overnight rate is the rate at which banks lend to each other overnight. Overnight index swaps (OIS) allow banks to 'lock in' the cost of funding overnight for a specific term. They ...
Dom's user avatar
  • 2,147
2 votes
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ICVS 133 Bloomberg Curve

ICVS 133 on BBG as a zero coupon curve for EUR OIS (so you wouldn't need to bootstrap). If you export to Excel, the discount factors are already in the exported sheet.
user42108's user avatar
  • 2,252
2 votes

Use Discrete ARMA(1,q) Process to Model Short Rate for Term Structure Fitting

You are describing something called Geometric Brownian Motion, and in the realm of short rates, you are describing the discretization short rates. For the Vasicek model, $R_t = aR_{t-1} + b +\epsilon$ ...
Mild_Thornberry's user avatar
2 votes
Accepted

Smile Dynamics - forward variance

Ok, so $$ d\xi_t^T = \omega e^{-k(T-t)} \xi_t^T dW_t $$ where $W$ is standard Brownian. Then, just by applying Ito I hope you can see that $$ \log \xi_t^T / \xi_0^T = \omega \int_0^t e^{-k(T-u)} dW_u -...
Frido's user avatar
  • 1,854
2 votes

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 ...
Rylan's user avatar
  • 430
1 vote

OIS rate to build Term structure

This is my most up-to-date understanding of the matter: (i) OIS Swaps are here to stay. Already today, in the US, there two types of OIS Swaps, ones indexed to the Effective Federal Funds Rate (EFFR) ...
Jan Stuller's user avatar
  • 6,098
1 vote
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Affine term structure for CDS

In a (very small) nutshell, the estimation idea is the following: Quoted CDS contracts are driven by a risk neutral default probability $PD_Q(\tau\leq T)$. The default probability is again modeled ...
Kermittfrog's user avatar
  • 6,628
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 ...
Dimitri Vulis's user avatar
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 ...
RWP - Down by the Bay's user avatar
1 vote

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

There is a lot of prepayment models for MBS, mostly every big bank has its own proprietary model. But the prepayment model can take into account many variables than only interest rate. A probability ...
Martin Vesely's user avatar

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