Questions tagged [interpolation]
The interpolation tag has no usage guidance.
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When getting the local vol surface from the implied vol surface, do we interpolate the strikes?
Using the dupire method:
$$\sigma(T, K)=\sqrt{\frac{\sigma_{\mathrm{imp}}^2+2 \sigma_{\mathrm{imp}} T\left(\frac{\partial \sigma_{\mathrm{imp}}}{\partial T}+(r-q) K \frac{\partial \sigma_{\mathrm{imp}}...
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Interpolating FRA curves for MPC dates
I have data for all the "white" FRAs with 3m fixings in a given market, i.e., 1x4 up to 9x12 and all the central back MPC meeting dates over the next twelve months.
What is the recommended ...
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Curve optimization to predict monetary policy path (OIS Curve)
This is a question about a relatively undeveloped market (Chile) in which Camara the O/N rate is daily compounded (OIS Curve).
The available instruments in the market are short term rates ie 1m 2m 3m ...
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Is there daily SPX level data going back to 1927?
While attempting to model the SPX index over time, I found a source here that purportedly has historical daily SPX data going back to 1789 which very likely seems to be backcasted since the ~500 stock ...
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1
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Zero Curve Interpolation Does Not recover Node point input rates
I having an issue with interpolation in QuantLib Python. Please see the code below for a minimum working example
...
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2
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167
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QuantLib: How to bootstrap Yield Curve using 3M futures - Python
I need to bootstrap a yieldcurve with 3M futures, using a cubic spline if possible.
Using, for example 3M Euribor, how do I bootstrap the yield curve using python?
I have a vector of dates and a ...
1
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1
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772
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Python yield curve bootstrapping equivalent to Matlab IRDataCurve.bootstrap
I want to bootstrap the yield curve of multiple currencies using 3M futures. I have it implemented in Matlab, but need to transfer to Python. I have a vector of dates and a vector of future prices.
...
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1
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505
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Graeme West's VBA code Monotone Convex
Can somebody post Graeme West's VBA code for monotone convex interpolation if you have? I was struggling to find it.
0
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1
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1k
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simple volatility surface interpolation
I'm trying to build an implied vol surface from some listed options. In particular I have data for calls and puts for different strikes and expiries. I'm not looking to price on the interpolated vols ...
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1
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201
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Quantlib Piecewise CubicZero Bond Curve Bootstrap
I am looking for more details on Piecewise Cubic Zero for bootstrapping/interpolating treasury curve ? Does quantlib uses Cubic interpolation or Cubic Spline interpolation ? If Cubic interpolation ...
1
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0
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Techniques for proxying time series / stock prices
What are some good techniques for proxying time series?
My purpose is for risk management / modelling and I would like proxy to missing series.
Given that I also have to account for volatility, ...
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175
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UnivariateSpline Spline Interpolation behaving erratically
I am using univariate spline to interpolate betweeen a number of dots I have (in blue - it is a yield curve). The code is the following:
...
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1
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86
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How do people 'lookup' values from calculated surfaces?
I have been wondering how the following situation is / should be implemented.
Consider some kind of surface $z = f(x,y)$ which has to be pre-calculated; the shape of this surface would not have a ...
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84
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Dividend adjustment on SABR formula for interpolating implied volatility
We are using a SABR model to interpolate the implied volatility surface.
The model yields a formula for implied volatility that contains the following term:
$\ln \left(\frac{K}{F}\right)$
It is ...
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What kind of interpolation is this?
I have Wiener process $W_t=\int_0^t\sigma(t)dB(t)$ where $B(t)$ - Brownian Motion and $\sigma(t)$ - piecewise constant function. I also take $t_k<t<t_{k+1}$ where I know the values of $W_{t_k}$ ...
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Interpolation and extrapolation of Discount factors
We are sourcing the discount factors for various currencies. What is the best interpolation method for dates between and out of the dates provided in the factors? Shall I go for flat forward or cubic ...
2
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1
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157
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Interpolation of $\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$
Let's assume that we have SDE
$$dX(t)=\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$$
and we simulate it on a time grid which contains points $t_k$ and $t_{k+1}$. How can we then calculate value of $X$ at time $...
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How do I calculate Hull White's Theta from the discount curve?
The Question
I'm currently implementing the a finite difference method for the Hull-White model, shown below:
$$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$
This ...
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What interpolation methods are standard to use for interpolating on equity volatility surfaces?
The answer to this question (Volatility surface interpolation for Black-Scholes delta hedging) names Cubic Spline Interpolation and Guassian Process interpolation (is this exactly the same thing as ...
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608
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Difference of polynomial interpolation for volatility smile
I am using 5 volatility points to build a volatility smile : put 10D, put 25D, ATMF, call 25D and call 10D. I have thus 5 pairs of data : (Delta, Vol) let's say for example (10;5.75) ; (25; 5.50) ; (...
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315
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Volatility surface interpolation for Black-Scholes delta hedging
A general question for interpolation method for implied volatility between tenors. I've recently stumbled accross a dataset from http://www.math.ku.dk/rolf/Svend/, and I would like to interpolate the ...
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3
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678
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Interpolating a yield from two yields (giving more weight to one of the two)
I would like some guidance with the following please.
Suppose I have two yields:
...
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289
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Practical implementation of Vellekoop-Nieuwenhuis model/interpolation
Have read the 2006 VELLEKOOP-NIEUWENHUIS paper (Efficient Pricing of Derivatives on Assets with Discrete Dividends) (Download) many times re Discrete dividends on American Options, but remain baffled ...
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Why use moneyness as an axis on a volatility surface
A simple volatility surface might have X axis = strike, Y axis = expiry and Z axis = implied volatility. But in many papers I see them use moneyness instead of strike. I have two questions.
Why do ...
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Any resources or literature on interpolation schemes for future dates?
I have a whole stack of the popular option trading/modelling books (Natenburg, Sinclair, Hull, etc.) None of them however address the idea of pricing or modelling values at a point in the "future&...
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Getting a daily forward OIS rate curve with QuantLib in Python
I am trying to build a 1-day EONIA forward curve with QuantLib giving OIS yields from 1mo to 50yr as input.
My current approach consists on (i) obtaining the yield curve with ...
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1
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631
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Simple approach to interpolate option surface
Let's set the spot price as 1 (spot price of underlying security) and express each option contract as a point in 3D space $$ \{ x, y, z \} = \{ tenor, moneyness, premium \} $$ where the premium is ...
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monotone convex interpolation using QuantLib
I have one yield curves for EUR6M and I want to produce EUR3M using a parallel shift to EUR6M curve.
I can just add spread in 6M curve. I am facing problem that my EUR3M curve will have many more ...
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2
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Quantlib ZeroCurve interpolation
I'd like to check how QuantLib does interpolation on rates if I use ZeroCurve constructor. As it was mentioned here, by using curve.nodes() you can get a list of ...
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Quantlib Natural Cubic spline yield curve
Is there an example to use Natural Cubic spline interpolation for yield curves in Quantlib python? I can see from the SWIG file that the interpolation is exposed but not sure how to use it.
I can ...
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Interpolation of SVI Implied Volatility in parameter space
I am currently working with a slice-wise SVI parametrisation of the implied volatility surface.
$\sigma^2(x,t) = a_t + b_t (\rho_t (x - m_t) + \sqrt{(x - m_t)^2 + \theta^2})$
Does anyone have ...
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What is the cause of a "broken" volatility surface?
I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
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2
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1k
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Linear Interpolation around End of Month (EOM) for IRS with standard rolls
I have a USD IRS S/A v 3M LIBOR with the following dates:
Effective: 30th April 2018
Maturity: 28th April 2028
(Rolls day of month = 28)
Therefore stub period runs from 30th April 2018 to 28th July ...
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1
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6k
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Quantlib-Python: use zero rates to get the originally bootstrapped curve
Let's say I am trying to build a curve using deposits, future and swaps with one of the three Quantlib methods in Python as below:
...
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Raw interpolation when the desired term is out of the know originals
I was reading this paper regarding the yield curve construction and was programming the Raw Interpolation algorithm (page 7 equation 6) however I was wondering how to use the formula when the desired ...
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1
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Getting option volatility off vol surface
I am currently looking into FX options. I am given a delta-tenor vol surface and I want to get the volatility of an option given its strike and time to expiry. I am reading about the method used and ...
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Estimating daily volatility of unevenly/irregularly spaced time series data
Say I have time-series data that is unevenly spaced, with anything between 4-50 hours of spacing in between. The data comes from a trading account history, which has captured the balance of the ...
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Interpolating cross-currency basis curve
Just wondering how do people "interpolate" between different "pillar dates" on a cross-currency basis curve? So say for example, if the observed spot is 1.5, observed CC basis for 9 months is -1.25 ...
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Excel Add-In Volatility Interpolation I am trying to Understand
The Microsoft Excel at my investment bank has an .xll add-in with a function whose coded functionality I cannot observe. This function is called VolInterp and as the name suggests, calculates the ...
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1
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3k
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Linear interpolation Discount factors
I am not sure how to perform a linear interpolation between discount fators for swap quotes. Lets say I have the following market quotes:
...
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683
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Ill-posed problem: Local volatility calibration. Regularization vs Smoothing
I have asked my question on Mathematics site of Stack Exchange but maybe I will get the answer rather here.
I am working on inverse problem - calibration of local volatility (financial application). ...
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Best method for interpolating yield curve? [Multiple questions]
I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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How does Bloomberg arrive at stub rate for swaps/floaters?
I'm trying to interpolate initial stub rate ( 'Index to' in the image ) for the following FRN pricing example.
Fixes on 2016/11/30
1m : 0.623670
2m : 0.742500
3m : 0.93417
Please be as specific as ...
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What techniques can be used to get the missing maturities from the CMT yields?
I have constant maturity treasury data from the h15 release of the FED, from which I use 6 month, 1 year, 2, 3, 5, 7, 10, and 20 year yields. I want to strip the zero coupon curve, but am not sure ...
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1
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Introducing 1bp shocks to yield curve (and interpolation consequences)
Let us assume we have a LIBOR 3M curve and that I would like to introduce a small shock up/down of 1bp at a certain point along the curve. I am trying to find out what the best and most efficient way ...
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Interpolation of forward zeros-coupons bonds simulations for missing maturities (ESG data)
I have a set of economic scenarios simulated with Barrie and Hibbert ESG. The stochastic model for interest rates used is Libor Market Model Shifted. I am facing a problem with zeros-coupons prices.
...
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Using Market Prices of Bonds to Model the Discount Curve with a Polynomial (Math + R)
I have a small program I'm building to interpolate the discount curve from a portfolio of benchmark bonds. If anyone has any guesses as to whether it's my process, or my code that's messed up I would ...
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Interpolating on the BS parameters and injecting in the BS formula vs interpolating directly on option prices
Let's consider a simple European call option. In practice, the way the Black-Scholes formula is used to price it is by injecting all of the parameters and paying special attention to the volatility ...
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1
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678
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Cubic spline interpolation function within Matlab
I want to use the Cubic spline interpolation technique so I can interpolate yield curve points. Now I wonder if I can use the standard matlab function interpl1 (and then using the 'spline' method) or ...
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Interpolation for PDF from Cumulative Distribution
How to interpolate PDF(Probability Distribution Functions) from CDF (without root finding method) ?
Please tell the steps to do so.
Thanks.
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