Class SmileSectionRNDCalculator

Namespace

NanoQL.Methods

Assembly

NanoQL.dll

The risk-neutral density of the logarithm of the underlying at a smile section's expiry, by the Breeden-Litzenberger identity: the density and distribution from the section's prices, the inverse from a table of log-moneyness against the normal quantile z = Φ⁻¹(P(S ≤ K)), linear for a lognormal law and well conditioned in the wings.

public sealed class SmileSectionRNDCalculator : RiskNeutralDensityCalculator

Inheritance

object

RiskNeutralDensityCalculator

SmileSectionRNDCalculator

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Immutable. The quantile table is built at construction (the playbook's LazyObject row), where QuantLib builds it at the first inverse; where it can't be built, the refusal is recorded and raised from InvCdf(double, double), QuantLib's point, since the density and distribution never need the table. Its argument x is ln(S); its only time is the section's exercise time.

Constructors

SmileSectionRNDCalculator(SmileSection, int, double)

Initializes a new instance of the SmileSectionRNDCalculator class.

public SmileSectionRNDCalculator(SmileSection smile, int nStrikes = 200, double nStd = 8)

Parameters

smile SmileSection

The smile section.

nStrikes int

The quantile table's size, at least 4.

nStd double

The table's half-width in normal quantiles, positive; the inverse saturates there, or at the deepest the smile still prices.

Exceptions

ArgumentNullException

smile is null.

ArgumentException

Fewer than 4 strikes, or a non-positive half-width, with QuantLib's messages.

Methods

Cdf(double)

The distribution function of ln(S) at the section's exercise time.

public double Cdf(double x)

Parameters

x double

The logarithm of the underlying.

Returns

double

The probability.

Cdf(double, double)

The distribution function of ln(S) at the section's exercise time, each tail from its own option type.

public override double Cdf(double x, double t)

Parameters

x double

The logarithm of the underlying.

t double

The time, the section's exercise time.

Returns

double

The probability.

Exceptions

ArgumentException

The time isn't the section's, with QuantLib's message.

InvCdf(double)

The inverse of the distribution function at the section's exercise time.

public double InvCdf(double p)

Parameters

p double

The probability, in (0, 1).

Returns

double

The logarithm of the underlying.

Exceptions

ArgumentException

The probability is outside (0, 1).

NanoQLException

The quantile table couldn't be built.

InvCdf(double, double)

The inverse of the distribution function at the section's exercise time, from the quantile table.

public override double InvCdf(double p, double t)

Parameters

p double

The probability, in (0, 1).

t double

The time, the section's exercise time.

Returns

double

The logarithm of the underlying.

Exceptions

ArgumentException

The time isn't the section's, or the probability is outside (0, 1), with QuantLib's messages.

NanoQLException

The quantile table couldn't be built: QuantLib's refusal, raised here, as QuantLib raises it.

Pdf(double)

The density of ln(S) at the section's exercise time.

public double Pdf(double x)

Parameters

x double

The logarithm of the underlying.

Returns

double

The density.

Pdf(double, double)

The density of ln(S) at the section's exercise time.

public override double Pdf(double x, double t)

Parameters

x double

The logarithm of the underlying.

t double

The time, the section's exercise time within QuantLib's close_enough.

Returns

double

The density.

Exceptions

ArgumentException

The time isn't the section's, with QuantLib's message.