A free/open-source library for quantitative finance
Reference manual - version 1.20
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A free/open-source library for quantitative finance
Reference manual - version 1.20
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Local volatility curve derived from a Black curve. More...
#include <ql/termstructures/volatility/equityfx/localvolcurve.hpp>
Inheritance diagram for LocalVolCurve:Public Member Functions | |
| LocalVolCurve (const Handle< BlackVarianceCurve > &curve) | |
TermStructure interface | |
| const Date & | referenceDate () const |
| the date at which discount = 1.0 and/or variance = 0.0 | |
| Calendar | calendar () const |
| the calendar used for reference and/or option date calculation | |
| DayCounter | dayCounter () const |
| the day counter used for date/time conversion | |
| Date | maxDate () const |
| the latest date for which the curve can return values | |
VolatilityTermStructure interface | |
| Real | minStrike () const |
| the minimum strike for which the term structure can return vols | |
| Real | maxStrike () const |
| the maximum strike for which the term structure can return vols | |
| Public Member Functions inherited from LocalVolTermStructure | |
| LocalVolTermStructure (BusinessDayConvention bdc=Following, const DayCounter &dc=DayCounter()) | |
| default constructor More... | |
| LocalVolTermStructure (const Date &referenceDate, const Calendar &cal=Calendar(), BusinessDayConvention bdc=Following, const DayCounter &dc=DayCounter()) | |
| initialize with a fixed reference date | |
| LocalVolTermStructure (Natural settlementDays, const Calendar &, BusinessDayConvention bdc=Following, const DayCounter &dc=DayCounter()) | |
| calculate the reference date based on the global evaluation date | |
| virtual | ~LocalVolTermStructure () |
| Volatility | localVol (const Date &d, Real underlyingLevel, bool extrapolate=false) const |
| Volatility | localVol (Time t, Real underlyingLevel, bool extrapolate=false) const |
| Public Member Functions inherited from VolatilityTermStructure | |
| VolatilityTermStructure (BusinessDayConvention bdc, const DayCounter &dc=DayCounter()) | |
| VolatilityTermStructure (const Date &referenceDate, const Calendar &cal, BusinessDayConvention bdc, const DayCounter &dc=DayCounter()) | |
| initialize with a fixed reference date | |
| VolatilityTermStructure (Natural settlementDays, const Calendar &cal, BusinessDayConvention bdc, const DayCounter &dc=DayCounter()) | |
| calculate the reference date based on the global evaluation date | |
| virtual BusinessDayConvention | businessDayConvention () const |
| the business day convention used in tenor to date conversion | |
| Date | optionDateFromTenor (const Period &) const |
| period/date conversion | |
| Public Member Functions inherited from TermStructure | |
| TermStructure (const DayCounter &dc=DayCounter()) | |
| default constructor More... | |
| TermStructure (const Date &referenceDate, const Calendar &calendar=Calendar(), const DayCounter &dc=DayCounter()) | |
| initialize with a fixed reference date | |
| TermStructure (Natural settlementDays, const Calendar &, const DayCounter &dc=DayCounter()) | |
| calculate the reference date based on the global evaluation date | |
| virtual | ~TermStructure () |
| Time | timeFromReference (const Date &date) const |
| date/time conversion | |
| virtual Time | maxTime () const |
| the latest time for which the curve can return values | |
| virtual Natural | settlementDays () const |
| the settlementDays used for reference date calculation | |
| void | update () |
| Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| std::pair< iterator, bool > | registerWith (const ext::shared_ptr< Observable > &) |
| void | registerWithObservables (const ext::shared_ptr< Observer > &) |
| Size | unregisterWith (const ext::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
| virtual void | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| void | notifyObservers () |
| Public Member Functions inherited from Extrapolator | |
| void | enableExtrapolation (bool b=true) |
| enable extrapolation in subsequent calls | |
| void | disableExtrapolation (bool b=true) |
| disable extrapolation in subsequent calls | |
| bool | allowsExtrapolation () const |
| tells whether extrapolation is enabled | |
Visitability | |
| virtual void | accept (AcyclicVisitor &) |
| Volatility | localVolImpl (Time, Real) const |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef boost::unordered_set< ext::shared_ptr< Observable > > | set_type |
| typedef set_type::iterator | iterator |
Calculations | |
These methods must be implemented in derived classes to perform the actual volatility calculations. When they are called, range check has already been performed; therefore, they must assume that extrapolation is required. | |
| Protected Member Functions inherited from VolatilityTermStructure | |
| void | checkStrike (Rate strike, bool extrapolate) const |
| strike-range check | |
| Protected Member Functions inherited from TermStructure | |
| void | checkRange (const Date &d, bool extrapolate) const |
| date-range check | |
| void | checkRange (Time t, bool extrapolate) const |
| time-range check | |
| Protected Attributes inherited from TermStructure | |
| bool | moving_ |
| bool | updated_ |
| Calendar | calendar_ |
Local volatility curve derived from a Black curve.
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protectedvirtual |
The relation
\[ \int_0^T \sigma_L^2(t)dt = \sigma_B^2 T \]
holds, where \( \sigma_L(t) \) is the local volatility at time \( t \) and \( \sigma_B(T) \) is the Black volatility for maturity \( T \). From the above, the formula
\[ \sigma_L(t) = \sqrt{\frac{\mathrm{d}}{\mathrm{d}t}\sigma_B^2(t)t} \]
can be deduced which is here implemented.
Implements LocalVolTermStructure.
