Questions tagged [interpolation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
1 answer
252 views

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 votes
1 answer
471 views

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 ...
0 votes
1 answer
118 views

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 vote
0 answers
84 views

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, ...
  • 388
0 votes
0 answers
89 views

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: ...
  • 33
0 votes
1 answer
80 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
55 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 ...
  • 775
1 vote
1 answer
94 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 $W_{t_k}$ ...
  • 65
1 vote
1 answer
216 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
149 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 $...
  • 65
0 votes
1 answer
230 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
0 answers
261 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 ...
  • 832
0 votes
1 answer
375 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) ; (...
  • 108
0 votes
1 answer
211 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
3 answers
335 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: ...
  • 316
1 vote
0 answers
193 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 ...
  • 11
2 votes
2 answers
2k 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 votes
0 answers
62 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&...
  • 113
0 votes
1 answer
853 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
1 answer
429 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
1 answer
679 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 ...
  • 11
1 vote
2 answers
940 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 ...
  • 149
1 vote
1 answer
1k 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 ...
  • 692
0 votes
0 answers
367 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 ...
  • 113
1 vote
0 answers
147 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 ...
  • 146
2 votes
2 answers
955 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 ...
5 votes
1 answer
5k 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: ...
  • 559
0 votes
1 answer
152 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
1k 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 votes
1 answer
899 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
832 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 ...
  • 3
1 vote
1 answer
936 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
3k 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
588 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
14k 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 ...
  • 335
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
1k 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
289 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
157 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
166 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
840 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 ...
  • 165
2 votes
1 answer
644 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 ...
  • 325
1 vote
1 answer
280 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
93 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
0 answers
623 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
1k 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