Class SviSurface

java.lang.Object

com.quantfinlib.pricing.SviSurface

All Implemented Interfaces:

TotalVarianceSurface

public final class SviSurface
extends Object
implements TotalVarianceSurface

A surface of raw SVI slices (SviSlice), one per pillar expiry, interpolated linearly in total variance at fixed log-moneyness k = ln(K/F(t)).

Between pillars, w(t, k) = (1−u)·w₁(k) + u·w₂(k) with u = (t − t₁)/(t₂ − t₁). If the pillar slices do not cross (w₂(k) ≥ w₁(k) for all k) every interpolated w is non-decreasing in t, so the surface has no calendar arbitrage (Gatheral and Jacquier 2014, section 2, lemma 2.1 on total variance). Before the first pillar w = w₁(k)·t/t₁; after the last, w = w_n(k)·t/t_n (constant implied vol per k). Slice independence means crossing slices are possible: check with TotalVarianceSurface.calendarViolations(double[], double, double, int) or prefer SsviSurface, which is calendar-free by construction. Linear interpolation of two butterfly-free slices need not be butterfly-free; TotalVarianceSurface.minDensityFactor(double, double, double, int) checks it.

Constructor Summary

Constructors

Constructor	Description
SviSurface(double[] expiries, SviSlice[] slices, double spot, double rate, double carry)

Method Summary

Modifier and Type	Method	Description
static SviSurface	calibrate(double spot, double rate, double carry, double[] expiries, double[][] strikes, double[][] vols, double[][] weights)	Fits one SVI slice per expiry (SviSlice.calibrate(double[], double[], double[]), butterfly penalty on) to implied vol quotes.
double	carry()	Continuous carry yield (dividend yield, or foreign rate for FX).
double	expiry(int i)
int	expiryLength()
double	rate()	Continuously compounded risk-free rate.
SviSlice	slice(int i)
double	spot()	Spot price.
double	totalVariance(double t, double k)	Total implied variance at expiry t (years, > 0) and log-moneyness k.

Methods inherited from class Object

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

Methods inherited from interface TotalVarianceSurface

calendarViolations, forward, impliedVol, minDensityFactor, price

Constructor Details

SviSurface

public SviSurface(double[] expiries,
 SviSlice[] slices,
 double spot,
 double rate,
 double carry)

Method Details

calibrate

public static SviSurface calibrate(double spot,
 double rate,
 double carry,
 double[] expiries,
 double[][] strikes,
 double[][] vols,
 double[][] weights)

Fits one SVI slice per expiry (SviSlice.calibrate(double[], double[], double[]), butterfly penalty on) to implied vol quotes.

Parameters:

weights - residual weights per quote, or null for equal weights

expiryLength

public int expiryLength()

expiry

public double expiry(int i)

slice

public SviSlice slice(int i)

spot

public double spot()

Description copied from interface: TotalVarianceSurface

Spot price.

Specified by:

spot in interface TotalVarianceSurface

rate

public double rate()

Description copied from interface: TotalVarianceSurface

Continuously compounded risk-free rate.

Specified by:

rate in interface TotalVarianceSurface

carry

public double carry()

Description copied from interface: TotalVarianceSurface

Continuous carry yield (dividend yield, or foreign rate for FX).

Specified by:

carry in interface TotalVarianceSurface

totalVariance

public double totalVariance(double t,
 double k)

Description copied from interface: TotalVarianceSurface

Total implied variance at expiry t (years, > 0) and log-moneyness k.

Specified by:

totalVariance in interface TotalVarianceSurface