NAME

   VolSurface::Utils - A class that handles several volatility related
   methods

VERSION

   Version 1.00

SYNOPSIS

   A class that handles several volatility related methods such as gets
   strikes from a certain delta point, gets delta from a certain vol point
   etc.

    use VolSurface::Utils;

    my $delta = get_delta_for_strike({
               strike           => $strike,
               atm_vol          => $atm_vol,
               t                => $t,
               spot             => $spot,
               r_rate           => $r_rate,
               q_rate           => $q_rate,
               premium_adjusted => $premium_adjusted
             });

EXPORT

   get_delta_for_strike

   get_strike_for_spot_delta

   get_ATM_strike_for_spot_delta

   get_moneyness_for_strike

   get_strike_for_moneyness

   get_1vol_butterfly

   get_2vol_butterfly

METHODS

get_delta_for_strike

   Returns the delta (spot delta or premium adjusted spot delta)
   correspond to a particular strike with set of parameters such as atm
   volatility, time in year, spot level, rates

    my $delta = get_delta_for_strike({
               strike           => $strike,
               atm_vol          => $atm_vol,
               t                => $t,
               spot             => $spot,
               r_rate           => $r_rate,
               q_rate           => $q_rate,
               premium_adjusted => $premium_adjusted
   });

   Spot delta of an option is the percentage of the foreign notional one
   must buy when selling the option to hold a hedged position in the spot
   markets.

   Premium adjusted spot delta is the spot delta which adjusted to take
   care of the correction induced by payment of the premium in foreign
   currency, which is the amount by which the delta hedge in foreign
   currency has to be corrected.

get_strike_for_spot_delta

   Returns the strike corresponds to a particular delta (spot delta or
   premium adjusted spot delta) with a set of parameters such as option
   type, atm vol, time in year, rates and spot level.

    my $strike = get_strike_for_spot_delta({
               delta            => $delta,
               option_type      => $option_type,
               atm_vol          => $atm_vol,
               t                => $t,
               r_rate           => $r_rate,
               q_rate           => $q_rate,
               spot             => $spot,
               premium_adjusted => $premium_adjusted
           });

   Calculation of strike depends on which type of delta we have. Delta
   provided must be on [0,1].

get_ATM_strike_for_spot_delta

   Returns the ATM strike that satisifies straddle Delta neutral.

    my $atm_strike = get_ATM_strike_for_spot_delta({
           atm_vol => $atm_vol,
           t => $t,
           r_rate => $r_rate,
           q_rate => $q_rate,
           spot => $spot,
           premium_adjusted => $premium_adjusted,
       });

   The ATM volatility quoted in the market is that of a zero delta
   straddle, whose strike, for each given expiry, is chosen so that a put
   and a call have the SAME delta but with different signs. No delta hedge
   is needed when trading this straddle.

   The ATM volatility for the expiry T is the volatility where the ATM
   strike K must satisfy the following condition: Delta Call = - Delta Put

   The ATM strike is the strike correspond to this ATM volatility.

get_moneyness_for_strike

   Returns the corresponding moneyness point for a given strike.

    my $moneyness = get_moneyness_for_strike({
           strike => $strike,
           spot => $spot,
       });

get_strike_for_moneyness

   Returns the corresponding strike value for a given moneyness point.

    my $strike = get_strike_for_moneyness({
           spot => $spot,
           moneyness => $moneyness
       });

get_2vol_butterfly

   Returns the two vol butterfly that satisfy the abitrage free
   constraint.

    my $bf = get_2vol_butterfly($spot, $tiy,$delta, $atm, $rr, $bf, $r, $d, $premium_adjusted, $bf_style);

   DESCRIPTION: There are two different butterfly vol:

   -The first one is 2 vol butterfly which is the quoted butterfly that
   appear in interbank market (vwb= 0.5(Sigma(call)+SigmaP(Put))-
   Sigma(ATM)).

   -The second one is 1 vol butterfly which is the butterfly volatility
   that consistent with market standard conventions of trading the
   butterfly strategies (some paper called it market strnagle volatility).

   The market standard conventions for trading the butterfly is price the
   strangle with one unique volatility whereas with the first butterfly
   convention(ie the quoted butterfly vol), we will price the strangle
   with two volatility.

   There is possible arbitrage opportunities that might result from the
   inconsistency caused by the above quoting mechanism.

   Hence, in practice, we need to build a volatility smile so that the
   price of the two options strangle based on the volatility surface that
   we build will have same price as the one from the market conventional
   butterfly trading(ie with one unique volatility).

   The consistent constraint that need to hold in building surface is as
   shown as follow : C(K_25C, Vol_K_25C) + P(K_25P, Vol_K_25P) = C(K_25C,
   Vol_market_conventional_bf) + P(K_25P, Vol_market_conventional_bf)

   The first step in building the abitrage free volatility smile is to
   determine an equivalent butterfly which will combines with all the ATM
   and RR vol to yields a volatility smile that satisfies the above
   constraint .

   This equivalent butterfly which is also named as two vol butterfly or
   smiled butterfly can be found numerically.

   This is only needed if the butterfly is the 1 vol butterfly from the
   market without any adjustment yet. If vol smile is abitrage free, hence
   their BF is already adjusted accordingly to fullfill the abitrage free
   constraints, hence no adjustment needed on the BF.

   As this process gone through a numerical procedures, hence the result
   might be slightly different when compare with other vendor as they
   might used different approach to get the relevant result.

get_1vol_butterfly

   Returns the 1 vol butterfly which is the butterfly volatility that
   consistent with market standard conventions of trading the butterfly
   strategies (some paper called it market strnagle volatility)

    my $bf_1vol = get_1vol_butterfly({
               spot             => $volsurface->underlying->spot,
               tiy              => $tiy,
               delta            => 0.25,
               call_vol         => $smile->{25},
               put_vol          => $smile->{75},
               atm_vol          => $smile->{50},
               bf_1vol          => 0,
               r                => $volsurface->underlying->interest_rate_for($tiy),
               q                => $volsurface->underlying->dividend_rate_for($tiy),
               premium_adjusted => $volsurface->underlying->{market_convention}->{delta_premium_adjusted},
               bf_style         => '2_vol',
       });

AUTHOR

   Binary.com, <support at binary.com>

BUGS

   Please report any bugs or feature requests to bug-volsurface-utils at
   rt.cpan.org, or through the web interface at
   http://rt.cpan.org/NoAuth/ReportBug.html?Queue=VolSurface-Utils
   <http://rt.cpan.org/NoAuth/ReportBug.html?Queue=VolSurface-Utils>. I
   will be notified, and then you'll automatically be notified of progress
   on your bug as I make changes.

SUPPORT

   You can find documentation for this module with the perldoc command.

       perldoc VolSurface::Utils

   You can also look for information at:

     * RT: CPAN's request tracker (report bugs here)

     http://rt.cpan.org/NoAuth/Bugs.html?Dist=VolSurface-Utils
     <http://rt.cpan.org/NoAuth/Bugs.html?Dist=VolSurface-Utils>

     * AnnoCPAN: Annotated CPAN documentation

     http://annocpan.org/dist/VolSurface-Utils

     * CPAN Ratings

     http://cpanratings.perl.org/d/VolSurface-Utils

     * Search CPAN

     http://search.cpan.org/dist/VolSurface-Utils/

ACKNOWLEDGEMENTS

LICENSE AND COPYRIGHT

   Copyright 2015 Binary.com.

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