# Questions tagged [interpolation]

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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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0 votes
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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: ...
• 23
0 votes
1 answer
77 views

### 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 ...
• 143
1 vote
0 answers
41 views

### 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 ...
• 785
1 vote
1 answer
90 views

### 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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1 vote
1 answer
103 views

### 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 votes
1 answer
145 views

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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 ...
• 146
2 votes
2 answers
832 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
1 answer
4k 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: ...
• 519
0 votes
1 answer
131 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
1 answer
930 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 ...
• 71
4 votes
1 answer
702 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 ...
• 227
0 votes
1 answer
758 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
1 answer
830 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
1 answer
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: ...
• 220
3 votes
0 answers
533 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). ...
9 votes
2 answers
13k 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 ...
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1 vote
1 answer
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 ...
• 46
3 votes
1 answer
992 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
1 answer
276 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 ...
• 463
2 votes
0 answers
153 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 votes
0 answers
157 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
1 answer
788 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 ...
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2 votes
1 answer
622 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 ...
• 303
1 vote
1 answer
268 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.
• 75
3 votes
3 answers
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): ...
• 274
1 vote
1 answer
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, ...
• 463
2 votes
0 answers
90 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 ...
• 133
2 votes
0 answers
612 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 ...
• 793
1 vote
1 answer
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 ...
• 793
11 votes
2 answers
1k 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 ...
• 131
2 votes
3 answers
971 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). ...
• 139
2 votes
0 answers
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 ...
• 153
3 votes
1 answer
162 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= -...
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