Class LocalVolMonteCarlo

java.lang.Object

com.quantfinlib.pricing.LocalVolMonteCarlo

public final class LocalVolMonteCarlo
extends Object

Monte Carlo under Dupire local volatility, log-Euler scheme:

  X_{n+1} = X_n + (r − q − ½σ_n²) Δt + σ_n √Δt Z_n,   σ_n = σ_loc(t_n, e^{X_n}),   X = ln S

(Glasserman 2003, Monte Carlo Methods in Financial Engineering, section 6.1). With constant σ the scheme is exact in distribution. The local vol at each step is read from a table of GRID_POINTS log-moneyness nodes spanning ±8 ATM standard deviations of the final expiry, linearly interpolated and held flat beyond; the table is built once per call. Antithetic pairs; seeded SplittableRandom, so a given seed reproduces the same price.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	LocalVolMonteCarlo.Result	Price and its Monte Carlo standard error.

Field Summary

Fields

Modifier and Type	Field	Description
static final int	GRID_POINTS	Local vol table size per time step.

Constructor Summary

Constructors

Constructor	Description
LocalVolMonteCarlo(DupireLocalVol localVol)

Method Summary

Modifier and Type	Method	Description
LocalVolMonteCarlo.Result	price(BlackScholes.OptionType type, double strike, double expiry, int pathPairs, int steps, long seed)	European option price.

Methods inherited from class Object

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

Field Details

GRID_POINTS

public static final int GRID_POINTS

Local vol table size per time step.

See Also:

• Constant Field Values

Constructor Details

LocalVolMonteCarlo

public LocalVolMonteCarlo(DupireLocalVol localVol)

Method Details

price

public LocalVolMonteCarlo.Result price(BlackScholes.OptionType type,
 double strike,
 double expiry,
 int pathPairs,
 int steps,
 long seed)

European option price.

Parameters:

pathPairs - number of antithetic pairs (≥ 1)

steps - time steps (≥ 1)