VIP 2.0
Next Generation
Volatility InterPolation
VIP 2.0 - Load Page
See input data
in detail
Click two buttons
to start game
VIP 2.0 is also available with
real-time data connection
See, what input data is
available for a given
underlying
VIP 2.0 - On-the-Fly Calculation
Get option grid filled +
your extra grid-points…
Hit Calc to create
a single surface
Choose
underlying
Type of surface and
cleansing parameters
Detailed output file
VIP 2.0 - Batch Calculation
Holds the extra grid
for all underlyings
Holds
parameters for
batch run
File-based Inputs
adjust settings for surface
Find detailed
output here
Hit Calc to run
batch
global options for
batch run
BASF Put Surface
Stochastic model recognizes a
“smile”
“smile”inininput
quotes
data(black)
(black)and
and
extrapolates accordingly (green)
VIP 2.0 uses extrapolation based on
a stochastic volatility model. It is
able to fit a large number of input
patterns and fails over to special
splines for the remainder
Black dots mark the
option quote input
Underlying: BASF
Option Type: Put
Spot: 50.33 €
Time Stamp: 11/10/2011 16:27
Interpolated gridpoints (also green)
E-Stoxx Call Surface
Input curvature fits a
”smile”, here …
Underlying: EURO STOXX
Option Type: Call
Spot: 2504.49
Time Stamp: 2/6/2012 16:25
The stochastic vol model is able to
recognize different patterns in the
input of a single surface.
… but rather a (moderate)
“skew”, here
… and even a (moderate)
“frown”, here
E-Stoxx X-over Surface (Put and Call)
Underlying: EURO STOXX
Option Type: X-over (Put and Call)
Spot: 2254.01
Time Stamp: 11/10/2011 16:25
B&C X-over produces a single
arbitrage-free vol surface from put
and call options simultaneously. Outof-the-money options are weighted
heavier than in-the-money options
using the option delta as driving
parameter
VIP 2.0 handles arbitrage afflicted input
Deutsche Bank
Option Type: Call
Spot: 38.66€
Time Stamp: 03/16/2012 16:27
Quoted option vols contain
arbitrage. The VIP surface is
calculated on an optimal arbitragefree trade-off. Hence, it is obliged
to leave some points manifestly off
the surface.
Arbitrage Correction (II)
VIP 2.0 output comes always with an arbitrage measure, which is the maximum riskless gain
obtainable from the 5 trading strategies that enforce the 5 arbitrage conditions. Positive values
indicate arbitrage opportunities. This example of calendar arbitrage is particularly easy, since the
arbitrage measures coincides with price differences.
VIP vol does not allow for a
riskless gain:
Quoted Vol arbitrage relative
to VIP Vol surface:
Calendar arbitrage yields
riskless gain of
17.217€ - 17.291€ = - 0.074€
17.51€ - 17.291€ = 0.219€
17.51€ - 16.98€ = 0.53€
17.217€ - 16.98€ = 0.237€
VIP eliminates arbitrage of Quoted Option Prices
How come B&C dares to talk about
“Next Generation”?
•
•
•
Simply, because we claim we have the next
generation answer to the four long standing
problems of volatility surface calculation (see next
slide).
In total, VIP 2.0 delivers features in a numerically
accessible way that have been reach-able (if at
all?) only at tremendous numerical effort
We suggest a scientific and practicable way to
extrapolation that brings about a dramatic numerical advantage enabling us to enforce all strike and
calendar no-arbitrage conditions in one go.
The „Big 4“ of Vola Surface Calculation
Only options for some strike maturity pairs are quoted –
often not the ones needed. A volatility surface is always a
Sparse Grid Problem that leads to very badly conditioned
matrices when an optimization shall be carried out.
II. Even less options are really liquid. A “simultaneous” option
quotes snapshot leads to rather Polluted Input Data.
III. There is no commonly agreed way, how to extrapolate
volatility in (a) scientific way, (b) at acceptable numerical
costs and (c) for any given input dataset and.
IV. Options prices can contain arbitrage, which is difficult to
spot or avoid numerically in volatility space. There are 4
arbitrage conditions in strike plus one calendar arbitrage
condition in time dimension.
I.
How we tackle Polluted Input Data (II):
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•
•
•
Benoist & Company is a Market Data Company.
We have tremendous experience in setting up
market data solutions and satisfying all sorts of
data cleansing needs.
Thus, VIP 2.0 comes equipped with sophisticated
and well-tested data cleansing mechanisms
based on our large in-house expertise.
The cleansing criteria can be adjusted by the
user to obtain best data quality from given option
quote inputs.
Default parameters for cleansing have been
calibrated on a very large number of input quote
sets.
How we tackle the Sparse Grid (I):
•
•
•
In principle it is easy to fill a surface, but if no-arbitrage
conditions have to be met by a non-trivial optimization the
resulting matrix is very poorly conditioned. This forced
prior solutions (Fengler, etc) to do the optimization tenorwise and put up with non unique solutions and failing
optimizations.
Our trick is to do the extrapolation of a so called “target”
first, create a well conditioned optimization matrix. We
are then able to enforce all arbitrage conditions in strike
and calendar direction (2D) at a time for the whole grid.
Thus, VIP 2.0 generates plausible vola surfaces for any
user-supplied grid - reproducing “good” option quotes
with high accuracy (<1bp).
How we tackle extrapolation (III)
•
•
•
•
Early extrapolation was seen as pure data fitting problem
which lead to “nice” surfaces but lacked “scientific”
foundation on the basis of any financial model.
Stochastic vol models published over the last decade were
successful in explaining volatility patterns but often not
practicable for near-time calculations and – even worse –
there is no model that can fit to all observable inputs.
VIP 2.0 uses a carefully designed extrapolation
technique employing a stochastic vol model (Heston) to
provide extrapolations based on financial mathematics.
We chose a parameterization that is numerically efficient
and reproduces a large number of input patterns
For the remainder of situations we found an ultra-robust
extrapolation based on special surface splines that avoids
problems (like wiggles or implausible behavior) present in
previously suggested approaches.
How we tackle arbitrage (IV)
•
•
•
Algorithms that enforce arbitrage in price space
have to transform as last step prices into BS-Vol.
This introduced minimal arbitrage in the order of
magnitude of the numerical error, but made
results worthless for model calibrations.
So practitioners calculated in vola space with
tremendous numerical effort.
We are able to align the numerical effort and
distance from the arbitrage boundary. Together
with the well conditioned optimization matrix (see
(I) VIP 2.0 is the first tool to produce a unique,
100% arbitrage free solution, quicker than 1
sec (on average on a single processor)
Further Benefits
• VIP 2.0 is designed to handle on the fly calculations, file-based bulk
processing, as well as continuous near-time processing in
connection with real-time data provision
• Comes as C++ standalone with its GUI. Algorithm is encapsulated
and can be incorporated in many other systems.
• It allows for 3D visualization and comparison with external vol
surfaces
• It is optimal for arbitrage detection and allows to trace back to the
option input
• Extrapolation of volatilities to extremely short and extremely long
expiries
• Reproduces market implied volatilities very well (up to ca. 1 bp)
• Pricing of any strike/maturity combination
• And the best: VIP comes at a true one-to-many price
Contact
• Contact:
Benoist & Company GmbH
Seefelder Str. 15
82229 Seefeld
Germany
Mail: contact@benoist-company.com
Web: www. benoist-company.com
Tel.: +49 8152 99 81 82
Fax.: +49 8152 99 81 83