NAME

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

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 ($strike, $atm_vol, $t, $spot, $r_rate, $q_rate, $premium_adjusted) = (); ## initialize args
        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,
            forward          => $forward
        });

    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. 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

      * 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.

