Skip to main content

Questions tagged [interpolation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2 votes
0 answers
51 views

Interpolating the volatility cube of European Swaptions

I'm in a situation where I have a cube of European swaption volatilities (normal volatilities), which contains only scattered data. Since it is three dimensional (Tenor, Term, Strikes) I'm having a ...
Leoncino's user avatar
  • 161
0 votes
1 answer
82 views

Interpolation of IV based on delta

I have a dataset with options, all the same date and time to maturity but different IV and delta. Now, I want to find the IV for certain delta values (e.g 0.5) through interpolation. Do you think that ...
Masmar's user avatar
  • 1
0 votes
1 answer
76 views

Double interpolation continuity

I am trying to use double interpolation(linear and forward quartic) but the interpolator is the zero coupon so at each time i need to convert the instantaneous forward rate to zc my problem is at the ...
Bred 's user avatar
0 votes
1 answer
59 views

Interpolation of term structure of implied volatility

I have a dataset of options traded at each day, including the time to maturity, delta, strike price etc. Now I want to get the implied volatility of an option with time to maturity 30 days through ...
Masmar's user avatar
  • 1
1 vote
0 answers
59 views

How to determine a correct interpolation technique for discount factor curves?

I think Log-Linear interpolation of discount factor curve is most preferred. I think this is due to the fact of not having any arbitrages in the forward rates. Can someone share some literature or ...
RKG's user avatar
  • 11
0 votes
0 answers
20 views

FX portfolio MV estimation for undelying Spot move

In the context of a project involving FX derivatives, I am faced with the challenge of estimating the change in the market value of my portfolio in response to a change in the underlying spot. The ...
AIEA's user avatar
  • 21
2 votes
1 answer
114 views

Cubic Spline Interpolation partial derivative to the point

Still didn't figure out this, so looking for some help, kindly apppreciated. By this blog https://blog.timodenk.com/cubic-spline-interpolation/index.html, the piecewise cubic spline interpolation is ...
imyafeng's user avatar
0 votes
2 answers
129 views

how to make this time series reguarly spaced

in the picture below we have in the first coloumn the day of the month, in the second coloumn the time in millisecond in epoch time(elapsed from 1 january 1970), third coloumn the stock price and in ...
XY0's user avatar
  • 117
0 votes
2 answers
271 views

Bootstrapping the zero-curve/spot-curve from incomplete swap curve par-rates

TL;DR: I have an incomplete set of swap rates and want to bootstrap the zero-rate curve, what can I do? I'm trying to construct a spot-rate/zero-rate curve from a swap curve (i.e. par-rate quotes) ...
Energy Media's user avatar
0 votes
2 answers
110 views

Survival probability interpolation between two time nodes

In the Open Gamma paper describing the ISDA CDS pricing model, it is mentioned that given the time notes of the credit curve $T^c=\{t_{1}^{c},...,t_{n_{c}}^{c}\}$ and that the survival probability for ...
Whitebeard13's user avatar
1 vote
0 answers
189 views

Arbitrage-Free implied/local volatility surface with Cubic Spline Interpolation

I am trying to create a local volatility surface using a cubic spline interpolated implied volatility surface. In other words, I have a function $\sigma(T,K)$, that is arbitrage-free $\forall T,K$ (...
THATS MY QUANT MY QUANTITATIVE's user avatar
0 votes
0 answers
134 views

Methods for Constructing a Yield Curve

I wonder if the Raw interpolation (known as linear on the log of discount factors) can handle negative interest rate due to the inverted yield curve? I understand using the linear on log of rates and ...
Riskquant's user avatar
6 votes
0 answers
288 views

Creating the local volatility surface from the IV surface

I have been using the dupire equation: $$ \sigma_{LV} (K,T) = \frac{\sigma_{i m p}^2+2 \sigma_{i m p} T\left(\frac{\partial \sigma_{i m p}}{\partial T}+(r-q) K \frac{\partial \sigma_{i m p}}{\partial ...
Xerium's user avatar
  • 89
3 votes
0 answers
55 views

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}}...
Xerium's user avatar
  • 89
0 votes
0 answers
40 views

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 ...
Vladimir Nabokov's user avatar
0 votes
1 answer
70 views

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 ...
SwapperAtPar's user avatar
2 votes
0 answers
126 views

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 ...
QMath's user avatar
  • 249
1 vote
1 answer
111 views

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 ...
Tomi Adewusi's user avatar
2 votes
2 answers
468 views

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 ...
Afonso Batista's user avatar
2 votes
1 answer
1k views

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. ...
Afonso Batista's user avatar
0 votes
1 answer
614 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.
Sarat Muppana's user avatar
0 votes
1 answer
1k 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 ...
apocalypsis's user avatar
0 votes
1 answer
266 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 ...
Sarat Muppana's user avatar
1 vote
0 answers
109 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, ...
Landscape's user avatar
  • 548
0 votes
0 answers
191 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: ...
Fidelio's user avatar
  • 59
0 votes
1 answer
86 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 ...
Zac's user avatar
  • 197
1 vote
0 answers
99 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 ...
Joanna's user avatar
  • 863
1 vote
1 answer
108 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 $W_{t_k}$ ...
Markov's user avatar
  • 75
2 votes
1 answer
460 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 ...
Quant enthsiast's user avatar
2 votes
1 answer
164 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 $...
Markov's user avatar
  • 75
0 votes
1 answer
479 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 ...
user59093's user avatar
2 votes
0 answers
515 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 ...
Oscar's user avatar
  • 902
0 votes
1 answer
733 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) ; (...
Xomuama's user avatar
  • 128
0 votes
1 answer
361 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 ...
Sebastian Strauss Hansen's user avatar
1 vote
3 answers
975 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: ...
F0l0w's user avatar
  • 316
1 vote
0 answers
359 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 ...
bizmark's user avatar
  • 11
4 votes
2 answers
4k 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 ...
brownie74's user avatar
0 votes
0 answers
77 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&...
TCopple's user avatar
  • 113
0 votes
1 answer
1k 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 ...
Tomás Carrera de Souza's user avatar
1 vote
1 answer
732 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 ...
Alex Craft's user avatar
1 vote
1 answer
1k 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 ...
Devlife's user avatar
  • 11
2 votes
2 answers
2k 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 ...
kismsu's user avatar
  • 159
1 vote
1 answer
2k 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 ...
InnocentR's user avatar
  • 692
0 votes
0 answers
571 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 ...
Michael's user avatar
  • 133
1 vote
0 answers
170 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 ...
10uss's user avatar
  • 156
2 votes
2 answers
1k 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 ...
Monsieur Crumbs's user avatar
5 votes
1 answer
6k 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: ...
opt's user avatar
  • 559
0 votes
1 answer
187 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 ...
Alejandro Andrade's user avatar
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 ...
acchan94's user avatar
4 votes
1 answer
1k 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 ...
Doggie52's user avatar
  • 227