6 votes

Interpolation of $\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$

That is a tricky question because interpolation seems to be ok if you need one point $\tau$ between $t_k$ and $t_{k+1}$ but it is not. The difficulty arise a direct way if you want two points inside $[...
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  • 10.5k
6 votes
Accepted

Quantlib-Python: use zero rates to get the originally bootstrapped curve

To retrieve the original curve, you need to use the same key tenors of the original curve and with the same interpolation. For instance, when you create the original curve as: ...
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5 votes

Best method for interpolating yield curve? [Multiple questions]

Typically, the yield curve used for performing relative value analysis should be built from off-the-run bonds. Different vendors select different bonds, but starting with all outstanding Treasury ...
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  • 10.9k
4 votes

Why use moneyness as an axis on a volatility surface

First off, there are different types of moneyness one can use when constructing a volatility surface. Each have their own advantages. Absolute-moneyness: using absolute spot-strike comparison as a ...
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4 votes

Why use moneyness as an axis on a volatility surface

If you use constant strike, the moneyness changes as the underlying changes. Out of the money equity options tend to trade at a premium to at the money options (smiles/skew). Therefore, the ...
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  • 5,030
3 votes
Accepted

Difference of polynomial interpolation for volatility smile

This is not really an answer but it's too long for a comment. The lagrange / cublic spline interpolation is very sensitive to the input data, given slightly different input data it can produce vastly ...
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  • 726
3 votes
Accepted

Excel Add-In Volatility Interpolation I am trying to Understand

They are lineary interpolating in total variance. I find the exact same answer as your add-in function returns. In other words the interpolation is made wrt time and between $z_1 = T_1 \times v_1 \...
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  • 1,346
3 votes
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How does Bloomberg arrive at stub rate for swaps/floaters?

Basic money markets arithmetic. Using day count convention ACT/ACT, 01 Dec 2016 to 13 Jan 2017 is 43 days, ...
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  • 929
3 votes
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What techniques can be used to get the missing maturities from the CMT yields?

The CMT yields published by the Fed/US Treasury are par yields calculated using a cubic spline model. In other words, these are the yields to maturity as well as coupon rates on bonds whose theoretic ...
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  • 10.9k
3 votes

Interpolation on CDS rates

There is no such thing as a "proper" interpolation of CDS spreads. The only criterium your interpolation must obey is the absence of arbitrage. Note that, assuming that $spread(3M) < spread(6M)$, ...
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  • 346
3 votes

Smoothing Term Curve

There are quite a few strategies you could take. Use models that are more resistant to noises. As others have already mentioned, parametric models such as Nelson-Siegel or Svensson may do the trick. ...
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  • 10.9k
3 votes

Interpolation and extrapolation of Discount factors

Be careful with various naive smooth interpolations of discount factors that are easy to screw up and may lead to unrealistic rates between the nodes. But your choice depends on your planed usage. If ...
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2 votes
Accepted

Interpolating probabilities of default

I believe that your problem can be formulated as: Find PD matrix that is as close as possible to a given PD matrix (result of some previous calibration, or the matrix computed using average hazard ...
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  • 346
2 votes

Interpolating on the BS parameters and injecting in the BS formula vs interpolating directly on option prices

The best way is to interpolate in volatility space. The reason is because it is closer to the intrinsic pricing of the option, and it is less likely to produce an arbitrage. Like Alex C noted in the ...
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2 votes

Quantlib ZeroCurve interpolation

The data stored in the object is adjusted such that compounding is Continuous and frequency is NoFrequency. The C++ source code ...
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  • 730
2 votes

Getting option volatility off vol surface

See the paper "FX Volatility Smile Construction, Dimitri Reiswich and Uwe Wystup" http://janroman.dhis.org/finance/FX/FX%20Volatility%20Smile.pdf for a comprehensive construction of the FX volatility ...
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2 votes

Simple approach to interpolate option surface

As has been said in the comments, unless you are working with an asset class that has a second dimension, i.e, swaptions where you have not only the option expiry but also the underlying tenor, a ...
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  • 5,285
2 votes
Accepted

What kind of interpolation is this?

I don't understand why they not just use $$\tag{1} D=\sigma^2(t_k)(t_{k+1}-t_k) $$ which leads to the theoretically correct variance of $W_t-W_{t_k}$. Rewriting (3) gives for the increment over the ...
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  • 1,429
2 votes

How do people 'lookup' values from calculated surfaces?

A linear interpolation in 2d is not much more complicated that in 1d: \begin{align} \color{red}{f(x,y_i)}&=\frac{f(x_i,y_i)(x_{i+1}-x)+f(x_{i+1},y_i)(x-x_i)}{x_{i+1}-x_i}\,,\\[3mm] \color{red}{f(x,...
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  • 1,429
1 vote

How do I calculate Hull White's Theta from the discount curve?

In practical situations you will never know $P^M(0,t\pm\epsilon)$ for a continuum of $t$ and $\epsilon\,.$ In other words, $\theta$ will practically always depend on an interpolation method between ...
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  • 1,429
1 vote
Accepted

Volatility surface interpolation for Black-Scholes delta hedging

A cubic polynomial curvature would be the most simple one.Otherwise,many practitioners are actually using a Gaussian process interpolation,which is more sophisticated.
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  • 446
1 vote

Interpolating a yield from two yields (giving more weight to one of the two)

If these are risky (e.g., corporate) bullet bonds, then I would not interpolate the yield directly, because their yield has two distinct components: a risk-free rate and an additional spread (to ...
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1 vote

Getting a daily forward OIS rate curve with QuantLib in Python

The problem is that in the first step, you are only fetching the forwards for the curve nodes. You could make a daily schedule and get forwards directly from the curve for each date. ...
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  • 5,285
1 vote

monotone convex interpolation using QuantLib

Not sure why you would want this because you have quotes for EUR6M and EUR3M directly (Swap vs 3M and 3M Futures). Also not sure, why you would have more nodes for the 3M since both swaps and basis ...
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  • 5,285
1 vote
Accepted

Quantlib Natural Cubic spline yield curve

QuantLib has several interpolation methods for yield curves. Here is an example of a few methods for Portuguese Government Bonds to get you started. ...
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  • 5,285
1 vote

Linear Interpolation around End of Month (EOM) for IRS with standard rolls

The legal definition of the swap is given by the ISDA confirm which will specify “Floating Rate Option” USD Libor with a maturity of 3 months. If so, this means you always take 3month Libor no matter ...
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  • 13.7k
1 vote
Accepted

Raw interpolation when the desired term is out of the know originals

What you are interested in is called extrapolation. In other words, you want to "extend" your function $r$ for $t < t_0$ and $t > t_n$. What the author ...
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  • 1,209
1 vote
Accepted

Linear interpolation Discount factors

I don't recommend linear interpolation of DFs and the swap rates you are applying this to are either against 12M libor which is illiquid or you are not accounting for Quarterly or Semi-Annual floating ...
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  • 8,007
1 vote

Best method for interpolating yield curve? [Multiple questions]

A few observations: the coupon yield curve is never going to be smooth, because a high coupon Treasury and a low coupon Treasury with the same maturity do not yield the same. That's because in an ...
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  • 13.7k
1 vote

Introducing 1bp shocks to yield curve (and interpolation consequences)

The new curve will look a bit strange no matter how you do it, although 1bp is not such a big move that will render it "useless". Two ways of doing it, as you point out, are (a) use a spline method, ...
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