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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). The retrieval interfaces packaged with the market data API allow you to retrieve curves or surfaces 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 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()`.
`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`.
`IBicubicInterpolatorFactory`	Extends `IInterpolatorFactory`, `ICubic`, and `IBivariate`.
`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[][]`.

Several interpolators are provided in the com.activeviam.marketdata.lib.interpolation.interpolators.commonsmath.impl package.

Interpolator	Interpolation type	Axes	Interface	Details
`BicubicInterpolator`	`CUBIC`	2	`IInterpolator`, `ICubic`, `IBivariate`	Extends the Commons Math `BicubicIntepolator`.
`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.
`BicubicInterpolatorFactory`	`CUBIC`	1	`IBicubicInterpolatorFactory` (`IInterpolatorFactory`, `ICubic`, `IUnivariate`)	Constructs cubic interpolators that operate on a single axis.
`SplineBicubicInterpolatorFactory`	`SPLINE`	2	`ISplineBicubicInterpolatorFactory` (`IInterpolatorFactory`, `ISpline`, `IBivariate`)	Constructs spline interpolators that operate on two 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 a ConcurrentMap<Object, Object> cache 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(ConcurrentMap<Object, Object> cache, CompositeKey cacheKey, 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 autoconfigured.

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.
`BicubicInterpolatorConfig`	Publishes a `BicubicInterpolatorFactory` as an `IBicubicInterpolatorFactoryFactory` 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.