Interpolation APIs

The Atoti Market Data Library provides an interpolation API separated from the market data retrieval. The API is mostly contained in the market-data-lib module, with Spring configuration classes available in the market-data-spring-boot-starter module.

Supported interpolation types

This API supports linear, linear with volatility-to-variance transformations for surfaces, cubic and spline interpolation, with the InterpolationMode class in the com.activeviam.marketdata.lib.interpolation.services.intf package providing valid options.

Value	Details
InterpolationMode.LINEAR	Linear interpolation is required for missing data points.
InterpolationMode.VOL_TO_VARIANCE	Linear interpolation with volatility-to-variance/variance-to-volatility pre- and post-interpolation transformations is required for missing data points.
InterpolationMode.CUBIC	Cubic interpolation is required for missing data points.
InterpolationMode.SPLINE	Spline interpolation is required for missing data points.

Handling market data

The interpolation API expects the known data points to be expressed as an array of doubles with corresponding double arrays of coordinates (tenors/moneyness/maturities). The retrieval interfaces packaged with the market data API allow you to retrieve curves, surfaces, or cubes as values and associated coordinates.

Market data values are always expressed as doubles, whereas coordinates will likely be expressed as other data types, based on the structure of the underlying market data store. The ICubeMarketData, ICurveMarketData, and ISurfaceMarketData interfaces allow you to extract coordinates as doubles by providing a mapping function.

Interpolator Interfaces

Interpolators are objects that return an interpolated point when provided with correctly configured known data points and the required coordinates. All interpolators must implement the IInterpolator interface:

Method	Return type	Details
value(double... coordinates)	double	Returns the interpolated value given the coordinates. A helper default validateCoordinates(double... coordinates) method is provided on the IInterpolatorSettings interface (see below) to check the validity of the requested coordinates against the supported axes.

Each interpolator is constructed with a factory that formats the input data correctly for that specific interpolator. These factories implement the IInterpolatorFactory interface:

Method	Return type	Details
from(double[] values, double[]... coordinates)	IInterpolator	Sets up the interpolator with known data points. The implementation has to check that the number of coordinate arrays matches the result of getAxis().

Both IInterpolator and IInterpolatorFactory interfaces extend the IInterpolatorSettings interface, which contains methods that describe the type of interpolation handled by that interpolator.

Method	Return type	Details
getMode()	InterpolationMode	The type of interpolation performed by the interpolator object.
getAxis()	int	The number of axes of the known data points.

You can also find a number of convenient interfaces, which extend the IInterpolationSettings interface and provide common settings as default methods.

Interface	Details
IUnivariate	Returns 1 on getAxis().
IBivariate	Returns 2 on getAxis().
ITrivariate	Returns 3 on getAxis().
ILinear	Returns InterpolationMode.LINEAR on getMode().
IVolToVariance	Returns InterpolationMode.VOL_TO_VARIANCE on getMode().
ICubic	Returns InterpolationMode.CUBIC on getMode().
ISpline	Returns InterpolationMode.SPLINE on getMode().
ILinearUnivariateInterpolatorFactory	Extends IInterpolatorFactory, ILinear, and IUnivariate.
IBilinearInterpolatorFactory	Extends IInterpolatorFactory, ILinear, and IBivariate.
IVolToVarianceBilinearInterpolatorFactory	Extends IInterpolatorFactory, IVolToVariance, and IBivariate.
ITrilinearInterpolatorFactory	Extends IInterpolatorFactory, ILinear, and ITrivariate.
IBicubicInterpolatorFactory	Extends IInterpolatorFactory, ICubic, and IBivariate.
ITricubicInterpolatorFactory	Extends IInterpolatorFactory, ICubic, and ITrivariate.
ISplineUnivariateInterpolatorFactory	Extends IInterpolatorFactory, ISpline, and IUnivariate.
ISplineBicubicInterpolatorFactory	Extends IInterpolatorFactory, ISpline, and IBivariate.

Interpolation transformation

For some use cases, both the input data for an interpolator and the result of the interpolation need to be transformed. To simplify the creation and configuration of transformations, we provide the following classes:

Class	Details
IInterpolationTransformation<T, U>	An interface for an object that transforms a market data quote based on a coordinate.
VolatilityToVarianceTransformation	Applies the volatility-to-variance formula to a tenor and a market data quote.
VarianceToVolatilityTransformation	Applies the variance-to-volatility formula to a tenor and a market data quote.

Interpolator Implementations

The majority of interpolators provided in Atoti Market Data use the Apache Commons Math library. As the Apache library expects unflattened matrices, conversion and sorting is handled through data classes in the com.activeviam.marketdata.lib.interpolation.interpolators.commonsmath.data package:

Class	Input	Details
CurveInterpolationData	Tenors and values	Sorts the tenors as double[] and stores the associated values as double[].
SurfaceInterpolationData	Tenors, moneyness, and values	Sorts the tenors and moneyness as double[], and stores the associated values as double[][].
CubeInterpolationData	Tenors, moneyness, maturities, and values	Sorts the tenors, moneyness and maturities as double[], and stores the associated values as double[][][].

Several interpolators are provided in the com.activeviam.marketdata.lib.interpolation.interpolators.commonsmath.impl package. We do not provide a three-axis interpolator for SPLINE interpolation, as the Commons Math implementation is deprecated and considered invalid.

Interpolator	Interpolation type	Axes	Interface	Details
BicubicInterpolator	CUBIC	2	IInterpolator, ICubic, IBivariate	Extends the Commons Math BicubicIntepolator.
TricubicInterpolator	CUBIC	3	IInterpolator, ICubic, ITrivariate	Extends the Commons Math TricubicInterpolator.
SplineUnivariateInterpolator	SPLINE	1	IInterpolator, ISpline, IUnivariate	Extends the Commons Math SplineInterpolator.
SplineBicubicInterpolator	SPLINE	2	IInterpolator, ISpline, IBivariate	Extends the Commons Math PiecewiseBicubicSplineInterpolator.

Further, custom interpolators let you carry out linear interpolation on any number of axes. You can find them in the com.activeviam.marketdata.lib.interpolation.interpolators.impl package.

Interpolator	Interpolation type	Axes	Interface	Details
LinearInterpolator	LINEAR	any	IInterpolator, ILinear	Custom implementation of a linear interpolator.
PostTransformationLinearInterpolator	Any type configured to provide a post-transformation linear interpolator.	any	IInterpolator, ILinear	Custom implementation of a linear interpolator, which allows the definition of post-interpolation transformations on any axis.

Interpolator factories

The following interpolator factory classes are available. Implementations of IInterpolatorFactory are available in the same package and these construct interpolators that work along one, two, or three axes, as follows:

InterpolatorFactory	Interpolation type	Axes	Interface	Details
LinearUnivariateInterpolatorFactory	LINEAR	1	ILinearUnivariateInterpolatorFactory (IInterpolatorFactory, ILinear, IUnivariate)	Constructs linear interpolators that operate on a single axis.
BilinearInterpolatorFactory	LINEAR	2	IBilinearInterpolatorFactory (IInterpolatorFactory, ILinear, IBivariate)	Constructs linear interpolators that operate on two axes.
VolToVarianceBilinearInterpolatorFactory	VOL_TO_VARIANCE	2	IVolToVarianceBilinearInterpolatorFactory (IInterpolatorFactory, IVolToVariance, IBivariate)	Applies the volatility-to-variance pre-interpolation transformation to surface market data and constructs interpolators that apply the variance-to-volatility post-interpolation transformation on the tenor axis.
TrilinearInterpolatorFactory	LINEAR	3	ITrilinearInterpolatorFactory (IInterpolatorFactory, ILinear, ITrivariate)	Constructs linear interpolators that operate on three axes.
BicubicInterpolatorFactory	CUBIC	1	IBicubicInterpolatorFactory (IInterpolatorFactory, ICubic, IUnivariate)	Constructs cubic interpolators that operate on a single axis.
TricubicInterpolatorFactory	CUBIC	2	ITricubicInterpolatorFactory (IInterpolatorFactory, ICubic, IBivariate)	Constructs cubic interpolators that operate on two axes.
SplineBicubicInterpolatorFactory	SPLINE	2	ISplineBicubicInterpolatorFactory (IInterpolatorFactory, ISpline, IBivariate)	Constructs spline interpolators that operate on two axes.
SplineTricubicInterpolatorFactory	SPLINE	3	ISplineTricubicInterpolatorFactory (IInterpolatorFactory, ISpline, ITrivariate)	Constructs spline interpolators that operate on three axes.

Interpolation service

Two interpolation services are available:

• The IInterpolationService interface, with corresponding InterpolationService implementation, collects the interpolator factories and allows the retrieval of an interpolator for the given mode, values, and number of coordinate axes. The retrieved interpolator is constructed with the correct known data points.
• The ICachingInterpolationService interface, with corresponding CachingInterpolationService implementation, is constructed with an underlying IInterpolationService which it uses to retrieve interpolators, caching those interpolators within an IQueryCache for faster retrieval.

The interfaces can be found in the com.activeviam.marketdata.lib.interpolation.services.intf package with the implementations in the com.activeviam.marketdata.lib.interpolation.services.impl package.

Class	Details
IInterpolationService	Provides a single getInterpolator(InterpolationMode mode, double[] values, double[]... coordinates) method returning an IInterpolator.
InterpolationService	Implementation of IInterpolationService that stores a set of interpolators and returns the correct interpolator for the given mode, values, and number of coordinate axes.
ICachingInterpolationService	Provides a single getInterpolator(IQueryCache cache, InterpolationMode mode, double[] values, double[]... coordinates) method returning an IInterpolator.
CachingInterpolationService	Implementation of ICachingInterpolationService caches interpolator instances for fast retrieval.

Spring configuration classes

Several Spring configuration classes are provided in the com.activeviam.marketdata.autoconfigure.interpolation package of the market-data-spring-boot-starter module, providing interpolation services and interpolator factory Spring beans. When you add the starter as a dependency in your project, the AllInterpolatorsConfig class will be auto-configured.

Class	Details
AllMarketDataInterpolationConfig	Imports all other *InterpolatorConfig classes.
InterpolationServiceConfig	Collects all IInterpolatorFactory beans and publishes an IInterpolationService bean that can be overridden by creating a custom bean of the same type. A further ICachingInterpolationService bean is also provided.
LinearUnivariateInterpolatorConfig	Publishes a LinearUnivariateInterpolatorFactory as an ILinearUnivariateInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
BilinearInterpolatorConfig	Publishes a BilinearInterpolatorFactory as an IBilinearInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
VolToVarianceBilinearInterpolatorConfig	Publishes a VolToVarianceBilinearInterpolatorFactory as an IVolToVarianceBilinearInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
TrilinearInterpolatorConfig	Publishes a TrilinearInterpolatorFactory as an ITrilinearInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
BicubicInterpolatorConfig	Publishes a BicubicInterpolatorFactory as an IBicubicInterpolatorFactoryFactory bean that can be overridden by creating a custom bean of the same type.
TricubicInterpolatorConfig	Publishes a LinearTricubicInterpolatorFactory as an ITricubicInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
SplineUnivariateInterpolatorConfig	Publishes a SplineUnivariateInterpolatorFactory as an ISplineUnivariateInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.
SplineBicubicInterpolatorConfig	Publishes a SplineBicubicInterpolatorFactory as an ISplineBicubicInterpolatorFactory bean that can be overridden by creating a custom bean of the same type.