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,
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.