Class WhalleyWilmott

java.lang.Object
com.quantfinlib.hedging.WhalleyWilmott
public final class WhalleyWilmott extends Object
Whalley-Wilmott OPTIMAL hedge bands — the answer to the question every band hedger otherwise guesses: how wide should the no-trade band around delta be? Hedging continuously is bankruptcy by transaction costs; hedging never is a naked option. The asymptotic optimum (Whalley & Wilmott 1997, small proportional costs) puts the half-width at 
  band = ( (3/2) · k · S · Γ² / λ )^{1/3}
— wider when trading is expensive (k, the proportional cost) and when gamma churns the delta (Γ²), narrower when you are more risk averse (λ). The cube root is the interesting part: costs must move by 8x to move the band by 2x, which is why band width is remarkably stable across venues.

The POLICY is as important as the width: when the hedge drifts outside the band, trade back to the NEAREST EDGE, not to the center — hedging to delta itself throws away the band's whole point (you would pay the spread again on the next tick's drift). Zero gamma degenerates honestly: zero band, always hedge exactly to delta.

Pairs with the band executors: trading.AutoHedger and crb.CrbAutoHedger take a band as configuration — this class is where that number should come from. Asymptotic result: for very large costs or tiny risk aversion the expansion degrades (stated, not hidden). Static, deterministic, research lane.

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static final record 
    WhalleyWilmott.Action
    The rebalancing decision: trade (to the nearest edge) or hold.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    bandHalfWidth(double spot, double gamma, double costRate, double riskAversion)
    The optimal no-trade half-width around delta.
    static WhalleyWilmott.Action
    rebalance(double currentHedge, double delta, double bandHalfWidth)
    The hedge-to-the-edge policy: hold inside the band, trade to the NEAREST edge outside it.

    Methods inherited from class java.lang.Object

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

  • Method Details

    • bandHalfWidth

      public static double bandHalfWidth(double spot, double gamma, double costRate, double riskAversion)
      The optimal no-trade half-width around delta.
      Parameters:
      spot - underlying price, > 0
      gamma - book gamma (signed; only |Γ| matters), finite
      costRate - proportional transaction cost k (e.g. 0.0005 = 5 bps), > 0
      riskAversion - λ > 0 (bigger = tighter hedging)

    • rebalance

      public static WhalleyWilmott.Action rebalance(double currentHedge, double delta, double bandHalfWidth)
      The hedge-to-the-edge policy: hold inside the band, trade to the NEAREST edge outside it.
      Parameters:
      currentHedge - the position currently held against the book
      delta - the book's current delta (the band's center)
      bandHalfWidth - from bandHalfWidth(double, double, double, double), ≥ 0