Questions tagged [interpolation]
The interpolation tag has no usage guidance.
47
questions
0
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1answer
41 views
Interpolation method to convert a 1 month return to daily return, is LN the answer? [closed]
Monthly return is 3%. Days in mo = 30. Daily return is LN?
2
votes
1answer
136 views
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 $...
0
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0answers
19 views
Local volatilty models for fixed maturity curves with sparse equity data
I'm implementing an options analytics platform - with sparse market data going out a few months. Mostly equities and fx options. Building a fixed maturity curve like the one on quikstrike by bantix is ...
0
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1answer
81 views
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 ...
2
votes
0answers
82 views
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 ...
0
votes
1answer
154 views
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) ; (...
0
votes
1answer
117 views
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 ...
1
vote
3answers
178 views
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:
...
1
vote
0answers
95 views
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 ...
2
votes
2answers
1k views
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 ...
0
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0answers
51 views
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&...
0
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1answer
434 views
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 ...
1
vote
1answer
216 views
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 ...
1
vote
1answer
321 views
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 ...
1
vote
2answers
499 views
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 ...
1
vote
1answer
792 views
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 ...
0
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0answers
239 views
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 ...
1
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0answers
140 views
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 ...
2
votes
2answers
730 views
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 ...
4
votes
1answer
3k views
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:
...
0
votes
1answer
108 views
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 ...
1
vote
1answer
854 views
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 ...
4
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0answers
581 views
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 ...
0
votes
1answer
711 views
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 ...
1
vote
1answer
752 views
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 ...
2
votes
1answer
2k views
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:
...
3
votes
0answers
506 views
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). ...
8
votes
2answers
12k views
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 ...
1
vote
1answer
2k views
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 ...
3
votes
1answer
940 views
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 ...
2
votes
1answer
263 views
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 ...
2
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0answers
150 views
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.
...
2
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0answers
152 views
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 ...
0
votes
1answer
740 views
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 ...
2
votes
1answer
608 views
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 ...
1
vote
1answer
259 views
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.
3
votes
3answers
1k views
Interpolating probabilities of default
I have a table of cumulative probabilities of default of industrial bonds, in time and credit rating. It is similar to S&P whitepaper here. Basically, it looks like this (sample numbers):
...
1
vote
1answer
2k views
Interpolating spot rates given intermittent coupon-bond prices.
I'm trying to bootstrap spot rates given coupon-paying bond data. To simplify my problem, assume we are working with only 3 given data, the price/coupon rate on semi-annual bonds maturing in 0.5, 1, ...
2
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0answers
89 views
Multivariate interpolation for estimating FDM in-between grid points
After implementing some FDM to price some option, there are gaps between our grid points that may be of interest. From reading around, it appears common to use bilinear interpolation to estimate ...
2
votes
0answers
595 views
Funding spread in FVA calculation
For the FVA calculation, is the funding spread (either borrowing or lending) treated as a piecewise constant function (i.e., if the length of the exposure is 5 month and I know the 3 and 6 months ...
1
vote
1answer
1k views
Interpolation on CDS rates
I am just wondering if there is any way we could calculate a CDS Spread (not harzard rate) on a CDS curve. Most of the papers that I have come across so far discuss about interpolating the hazard ...
11
votes
2answers
981 views
Extrapolating implied volatilities to small time
Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 ...
2
votes
3answers
943 views
Smoothing Term Curve
Assume that we have current month term curve and the curves from the two previous months. The current curve may be shifted from the average of the previous two curve by some value (a parallel shift). ...
2
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0answers
1k views
Interpolate option volatility in delta space in R
I have a bunch of deltas and option implied vols at those deltas. I would like to interpolate them in R. Interpolating them in delta space seems difficult, since normally you would like the ATM calls ...
3
votes
1answer
161 views
Why for one year (and not two or three) government bonds (there is a spike for Switzerland & Denmark)?
On 10.10.2012, I have looked at the bond-rates and, both for Switzerland and Denmark, there is a discontinuity/spike at 1Y, as per below
Switzerland: ON= -0.09, 1W= -0.180, 1M= -0.230, 3M= -0.2, 6M= -...
11
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1answer
2k views
How do you estimate the volatility of a sample when points are irregularly spaced?
I was looking again at this question which basically haunts every quant I believe, and I was thinking about the effect of these gaps when computing volatility of the series.
Let's define the problem ...
14
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5answers
5k views
How to interpolate gaps in a time series using closely related time series?
I am trying to construct a daily time series of prices and returns for some large universe of securities. However, all I have available are a monthly time series of the prices/returns (as well as ...
