com.opengamma.strata.pricer.impl.option

Class SabrExtrapolationRightFunction

java.lang.Object

com.opengamma.strata.pricer.impl.option.SabrExtrapolationRightFunction

public final class SabrExtrapolationRightFunction
extends Object

Pricing function in the SABR model with Hagan et al. volatility function and controlled extrapolation for large strikes by extrapolation on call prices.

The form of the extrapolation as a function of the strike is \begin{equation*} f(K) = K^{-\mu} \exp\left( a + \frac{b}{K} + \frac{c}{K^2} \right). \end{equation*}

Benaim, S., Dodgson, M., and Kainth, D. (2008). An arbitrage-free method for smile extrapolation. Technical report, Royal Bank of Scotland.

OpenGamma implementation note: Smile extrapolation, version 1.2, May 2011.

Method Summary

Modifier and Type	Method and Description
double	getCutOffStrike() Gets the cut-off strike.
double	getMu() Gets the tail thickness parameter.
double[]	getParameter() Gets the three fitting parameters.
double[]	getParameterDerivativeForward() Gets the three fitting parameters derivatives with respect to the forward.
double[][]	getParameterDerivativeSabr() Gets the three fitting parameters derivatives with respect to the SABR parameters.
SabrFormulaData	getSabrData() Gets the underlying SABR data.
double	getTimeToExpiry() Gets the time to expiry.
static SabrExtrapolationRightFunction	of(double forward, double timeToExpiry, SabrFormulaData sabrData, double cutOffStrike, double mu) Obtains an instance with default volatility provider.
static SabrExtrapolationRightFunction	of(double forward, SabrFormulaData sabrData, double cutOffStrike, double timeToExpiry, double mu, VolatilityFunctionProvider<SabrFormulaData> volatilityFunction) Obtains an instance with volatility provider specified.
double	price(double strike, PutCall putCall) Computes the option price with numeraire=1.
ValueDerivatives	priceAdjointSabr(double strike, PutCall putCall) Computes the option price derivative with respect to the SABR parameters.
double	priceDerivativeForward(double strike, PutCall putCall) Computes the option price derivative with respect to the forward.
double	priceDerivativeStrike(double strike, PutCall putCall) Computes the option price derivative with respect to the strike.

Methods inherited from class java.lang.Object

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

Method Detail

of

public static SabrExtrapolationRightFunction of(double forward,
                                                double timeToExpiry,
                                                SabrFormulaData sabrData,
                                                double cutOffStrike,
                                                double mu)

Obtains an instance with default volatility provider.

The default volatility provider is SabrHaganVolatilityFunctionProvider.

Parameters:

forward - the forward

timeToExpiry - the time to expiration

sabrData - the SABR formula data

cutOffStrike - the cut-off-strike

mu - the mu parameter

Returns:

the instance

of

public static SabrExtrapolationRightFunction of(double forward,
                                                SabrFormulaData sabrData,
                                                double cutOffStrike,
                                                double timeToExpiry,
                                                double mu,
                                                VolatilityFunctionProvider<SabrFormulaData> volatilityFunction)

Obtains an instance with volatility provider specified.

Parameters:

forward - the forward

sabrData - the SABR formula data

cutOffStrike - the cut-off-strike

timeToExpiry - the time to expiration

mu - the mu parameter

volatilityFunction - the volatility function

Returns:

the instance

price

public double price(double strike,
                    PutCall putCall)

Computes the option price with numeraire=1.

The price is SABR below the cut-off strike and extrapolated beyond.

Parameters:

strike - the strike of the option

putCall - whether the option is put or call

Returns:

the option price

priceDerivativeStrike

public double priceDerivativeStrike(double strike,
                                    PutCall putCall)

Computes the option price derivative with respect to the strike.

The price is SABR below the cut-off strike and extrapolated beyond.

Parameters:

strike - the strike of the option

putCall - whether the option is put or call

Returns:

the option price derivative

priceDerivativeForward

public double priceDerivativeForward(double strike,
                                     PutCall putCall)

Computes the option price derivative with respect to the forward.

The price is SABR below the cut-off strike and extrapolated beyond.

Parameters:

strike - the strike of the option

putCall - whether the option is put or call

Returns:

the option price derivative

priceAdjointSabr

public ValueDerivatives priceAdjointSabr(double strike,
                                         PutCall putCall)

Computes the option price derivative with respect to the SABR parameters.

The price is SABR below the cut-off strike and extrapolated beyond.

Parameters:

strike - the strike of the option

putCall - whether the option is put or call

Returns:

the option and its derivative

getSabrData

public SabrFormulaData getSabrData()

Gets the underlying SABR data.

Returns:

the sabrData

getCutOffStrike

public double getCutOffStrike()

Gets the cut-off strike.

The smile is extrapolated above that level.

Returns:

the cutOffStrike

getMu

public double getMu()

Gets the tail thickness parameter.

Returns:

the mu parameter

getTimeToExpiry

public double getTimeToExpiry()

Gets the time to expiry.

Returns:

the time to expiry

getParameter

public double[] getParameter()

Gets the three fitting parameters.

Returns:

the parameters

getParameterDerivativeForward

public double[] getParameterDerivativeForward()

Gets the three fitting parameters derivatives with respect to the forward.

Returns:

the parameters derivative

getParameterDerivativeSabr

public double[][] getParameterDerivativeSabr()

Gets the three fitting parameters derivatives with respect to the SABR parameters.

Returns:

the parameters derivative