Package org.drip.xva.pde

Class ParabolicDifferentialOperator

java.lang.Object
org.drip.xva.pde.ParabolicDifferentialOperator
public class ParabolicDifferentialOperator
extends java.lang.Object
ParabolicDifferentialOperator sets up the Parabolic Differential Equation based on the Ito Evolution Differential for the Reference Underlier Asset, as laid out in Burgard and Kjaer (2014). The References are:

  • Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party Risk and Funding Costs Journal of Credit Risk 7 (3) 1-19
  • Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): Modeling, Pricing, and Hedging Counter-party Credit Exposure - A Technical Guide Springer Finance New York
  • Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk Risk 20 (2) 86-90
  • Li, B., and Y. Tang (2007): Quantitative Analysis, Derivatives Modeling, and Trading Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market World Scientific Publishing Singapore
  • Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing Risk 21 (2) 97-102




Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    ParabolicDifferentialOperator​(PrimarySecurity tradeable)
    ParabolicDifferentialOperator Constructor

  • Method Summary

    Modifier and Type Method Description
    PrimarySecurity asset()
    Retrieve the Tradeable Position
    double theta​(EvolutionTrajectoryVertex evolutionTrajectoryVertex, double positionValueVertex)
    Compute the Theta for the Derivative from the Asset Edge Value
    double[] thetaUpDown​(EvolutionTrajectoryVertex evolutionTrajectoryVertex, double positionValueVertex, double shift)
    Compute the Up/Down Thetas

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • ParabolicDifferentialOperator

      public ParabolicDifferentialOperator​(PrimarySecurity tradeable) throws java.lang.Exception
      ParabolicDifferentialOperator Constructor
      Parameters:
      tradeable - The Tradeable Position
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • asset

      public PrimarySecurity asset()
      Retrieve the Tradeable Position
      Returns:
      The Tradeable Position

    • theta

      public double theta​(EvolutionTrajectoryVertex evolutionTrajectoryVertex, double positionValueVertex) throws java.lang.Exception
      Compute the Theta for the Derivative from the Asset Edge Value
      Parameters:
      evolutionTrajectoryVertex - The Derivative's Evolution Trajectory Vertex
      positionValueVertex - The Position Value Vertex
      Returns:
      The Theta
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • thetaUpDown

      public double[] thetaUpDown​(EvolutionTrajectoryVertex evolutionTrajectoryVertex, double positionValueVertex, double shift)
      Compute the Up/Down Thetas
      Parameters:
      evolutionTrajectoryVertex - The Derivative's Evolution Trajectory Vertex
      positionValueVertex - The Asset Numeraire Vertex Value
      shift - The Amount to Shift the Reference Underlier Numeraire By
      Returns:
      The Array of the Up/Down Thetas