Class DeltaHedger

java.lang.Object

com.quantfinlib.hedging.DeltaHedger

public final class DeltaHedger
extends Object

Dynamic delta hedging simulator: sell an option, then replicate it by trading the underlying along a price path, rebalancing whenever the delta drifts outside a band. Quantifies the trade-off every option desk lives with — tighter bands mean smaller replication error but more transaction costs.

The final P&L is the hedging error: zero in the Black-Scholes limit of continuous, costless rebalancing at the true volatility; in practice it spreads with rebalancing interval, transaction costs, and the gap between implied and realized volatility.

Accounting: the premium goes into a cash account that compounds at rate; the shares held earn the continuous carry (paid into cash), consistent with the Black-Scholes-Merton drift r − q used for pricing (Hull, Options, Futures and Other Derivatives, ch. 17). Without the carry leg a q = 3% hedge would show a mean loss of roughly ∫ Δ·S·q dt.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	DeltaHedger.Config	Hedging settings.
static final record	DeltaHedger.HedgeReport

Method Summary

Modifier and Type	Method	Description
static DeltaHedger.HedgeReport	simulateShortOption(BlackScholes.OptionType type, double strike, double expiryYears, double rate, double carry, double hedgeVol, double[] path, double dtYears, DeltaHedger.Config config)	Simulates a short option delta-hedged along the given path.

Methods inherited from class Object

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

Method Details

simulateShortOption

public static DeltaHedger.HedgeReport simulateShortOption(BlackScholes.OptionType type,
 double strike,
 double expiryYears,
 double rate,
 double carry,
 double hedgeVol,
 double[] path,
 double dtYears,
 DeltaHedger.Config config)

Simulates a short option delta-hedged along the given path.

Parameters:

expiryYears - option expiry; should equal (path.length-1) * dtYears

rate - continuously compounded cash rate (annual)

carry - continuous yield paid by the underlying (dividend yield, or the foreign rate for FX), annual; it is credited to the hedge position each step

hedgeVol - volatility used for pricing and hedging (implied vol)

path - underlying prices; path[0] at inception, path[n-1] at expiry

dtYears - time between path points (e.g. 1/252 for daily)