/ 
Math-Business-BlackScholes-Binaries-1.22
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/ Math::Business::BlackScholes::Binaries

NAME

Math::Business::BlackScholes::Binaries

VERSION

Version 1.22

SYNOPSIS

use Math::Business::BlackScholes::Binaries;

# price of a Call option
my $price_call_option = Math::Business::BlackScholes::Binaries::call(
    1.35,       # stock price
    1.36,       # barrier
    (7/365),    # time
    0.002,      # payout currency interest rate (0.05 = 5%)
    0.001,      # quanto drift adjustment (0.05 = 5%)
    0.11,       # volatility (0.3 = 30%)
);

DESCRIPTION

Prices options using the GBM model, all closed formulas.

Important(a): Basically, onetouch, upordown and doubletouch have two cases of payoff either at end or at hit. We treat them differently. We use parameter $w to differ them.

$w = 0: payoff at hit time. $w = 1: payoff at end.

Our current contracts pay rebate at hit time, so we set $w = 0 by default.

Important(b) :Furthermore, for all contracts, we allow a different payout currency (Quantos).

Paying domestic currency (JPY if for USDJPY) = correlation coefficient is ZERO. Paying foreign currency (USD if for USDJPY) = correlation coefficient is ONE. Paying another currency = correlation is between negative ONE and positive ONE.

See [3] for Quanto formulas and examples

SUBROUTINES

vanilla_call

USAGE
my $price = vanilla_call($S, $K, $t, $r_q, $mu, $sigma)

DESCRIPTION
Price of a Vanilla Call

vanilla_put

USAGE
my $price = vanilla_put($S, $K, $t, $r_q, $mu, sigma)

DESCRIPTION
Price a standard Vanilla Put

call

USAGE
my $price = call($S, $K, $t, $r_q, $mu, $sigma)

PARAMS
$S => stock price
$K => barrier
$t => time (1 = 1 year)
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

DESCRIPTION
Price a Call and remove the N(d2) part if the time is too small

EXPLANATION
The definition of the contract is that if S > K, it gives
full payout (1).  However the formula DC(T,K) = e^(-rT) N(d2) will not be
correct when T->0 and K=S.  The value of DC(T,K) for this case will be 0.5.

The formula is actually "correct" because when T->0 and S=K, the probability
should just be 0.5 that the contract wins, moving up or down is equally
likely in that very small amount of time left. Thus the only problem is
that the math cannot evaluate at T=0, where divide by 0 error occurs. Thus,
we need this check that throws away the N(d2) part (N(d2) will evaluate
"wrongly" to 0.5 if S=K).

NOTE
Note that we have call = - dCall/dStrike
pair Foreign/Domestic

see [3] for $r_q and $mu for quantos

put

USAGE
my $price = put($S, $K, $t, $r_q, $mu, $sigma)

PARAMS
$S => stock price
$K => barrier
$t => time (1 = 1 year)
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

DESCRIPTION
Price a standard Digital Put

d2

returns the DS term common to many BlackScholes formulae.

expirymiss

USAGE
my $price = expirymiss($S, $U, $D, $t, $r_q, $mu, $sigma)

PARAMS
$S => stock price
$t => time (1 = 1 year)
$U => barrier
$D => barrier
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

DESCRIPTION
Price an expiry miss contract (1 Call + 1 Put)

[3] for $r_q and $mu for quantos

expiryrange

USAGE
my $price = expiryrange($S, $U, $D, $t, $r_q, $mu, $sigma)

PARAMS
$S => stock price
$U => barrier
$D => barrier
$t => time (1 = 1 year)
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

DESCRIPTION
Price an Expiry Range contract as Foreign/Domestic.

[3] for $r_q and $mu for quantos

onetouch

PARAMS
$S => stock price
$U => barrier
$t => time (1 = 1 year)
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

[3] for $r_q and $mu for quantos

notouch

USAGE
my $price = notouch($S, $U, $t, $r_q, $mu, $sigma, $w)

PARAMS
$S => stock price
$U => barrier
$t => time (1 = 1 year)
$r_q => payout currency interest rate (0.05 = 5%)
$mu => quanto drift adjustment (0.05 = 5%)
$sigma => volatility (0.3 = 30%)

DESCRIPTION
Price a No touch contract.

Payoff with domestic currency
Identity:
price of notouch = exp(- r t) - price of onetouch(rebate paid at end)

[3] for $r_q and $mu for quantos

upordown

USAGE
my $price = upordown(($S, $U, $D, $t, $r_q, $mu, $sigma, $w))

PARAMS
$S stock price
$U barrier
$D barrier
$t time (1 = 1 year)
$r_q payout currency interest rate (0.05 = 5%)
$mu quanto drift adjustment (0.05 = 5%)
$sigma volatility (0.3 = 30%)

see [3] for $r_q and $mu for quantos

DESCRIPTION
Price an Up or Down contract

common_function_pelsser_1997

USAGE
my $c = common_function_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w, $eta)

DESCRIPTION
Return the common function from Pelsser's Paper (1997)

get_stability_constant_pelsser_1997

USAGE
my $constant = get_stability_constant_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w, $eta, $p)

DESCRIPTION
Get the stability constant (Pelsser 1997)

ot_up_ko_down_pelsser_1997

USAGE
my $price = ot_up_ko_down_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w)

DESCRIPTION
This is V_{RAHU} in paper [5], or ONETOUCH-UP-KNOCKOUT-DOWN,
a contract that wins if it touches upper barrier, but expires
worthless if it touches the lower barrier first.

ot_down_ko_up_pelsser_1997

USAGE
my $price = ot_down_ko_up_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w)

DESCRIPTION
This is V_{RAHL} in paper [5], or ONETOUCH-DOWN-KNOCKOUT-UP,
a contract that wins if it touches lower barrier, but expires
worthless if it touches the upper barrier first.

get_min_iterations_pelsser_1997

USAGE
my $min = get_min_iterations_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w, $accuracy)

DESCRIPTION
An estimate of the number of iterations required to achieve a certain
level of accuracy in the price.

_get_min_iterations_ot_up_ko_down_pelsser_1997

USAGE
my $k_min = _get_min_iterations_ot_up_ko_down_pelsser_1997($S, $U, $D, $t, $r_q, $mu, $sigma, $w, $accuracy)

DESCRIPTION
An estimate of the number of iterations required to achieve a certain
level of accuracy in the price for ONETOUCH-UP-KNOCKOUT-DOWN.

_get_min_iterations_ot_down_ko_up_pelsser_1997

USAGE

DESCRIPTION
An estimate of the number of iterations required to achieve a certain
level of accuracy in the price for ONETOUCH-UP-KNOCKOUT-UP.

range

USAGE
my $price = range($S, $U, $D, $t, $r_q, $mu, $sigma, $w)

PARAMS
$S stock price
$t time (1 = 1 year)
$U barrier
$D barrier
$r_q payout currency interest rate (0.05 = 5%)
$mu quanto drift adjustment (0.05 = 5%)
$sigma volatility (0.3 = 30%)

see [3] for $r_q and $mu for quantos

DESCRIPTION
Price a range contract.

DEPENDENCIES

* Math::CDF
* Machine::Epsilon

SOURCE CODE

https://github.com/binary-com/perl-math-business-blackscholes-binaries

REFERENCES

[1] P.G Zhang [1997], "Exotic Options", World Scientific Another good refernce is Mark rubinstein, Eric Reiner [1991], "Binary Options", RISK 4, pp 75-83

[2] Anlong Li [1999], "The pricing of double barrier options and their variations". Advances in Futures and Options, 10, 1999. (paper).

[3] Uwe Wystup. FX Options and Strutured Products. Wiley Finance, England, 2006. pp 93-96 (Quantos)

[4] Antoon Pelsser, "Pricing Double Barrier Options: An Analytical Approach", Jan 15 1997. http://repub.eur.nl/pub/7807/1997-0152.pdf

AUTHOR

binary.com, <rohan at binary.com>

BUGS

Please report any bugs or feature requests to bug-math-business-blackscholes-binaries at rt.cpan.org, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math-Business-BlackScholes-Binaries. 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 Math::Business::BlackScholes::Binaries

You can also look for information at:

LICENSE AND COPYRIGHT

Copyright 2014 binary.com.

This program is free software; you can redistribute it and/or modify it under the terms of the the Artistic License (2.0). You may obtain a copy of the full license at:

http://www.perlfoundation.org/artistic_license_2_0

Any use, modification, and distribution of the Standard or Modified Versions is governed by this Artistic License. By using, modifying or distributing the Package, you accept this license. Do not use, modify, or distribute the Package, if you do not accept this license.

If your Modified Version has been derived from a Modified Version made by someone other than you, you are nevertheless required to ensure that your Modified Version complies with the requirements of this license.

This license does not grant you the right to use any trademark, service mark, tradename, or logo of the Copyright Holder.

This license includes the non-exclusive, worldwide, free-of-charge patent license to make, have made, use, offer to sell, sell, import and otherwise transfer the Package with respect to any patent claims licensable by the Copyright Holder that are necessarily infringed by the Package. If you institute patent litigation (including a cross-claim or counterclaim) against any party alleging that the Package constitutes direct or contributory patent infringement, then this Artistic License to you shall terminate on the date that such litigation is filed.

Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT HOLDER AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES. THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT PERMITTED BY YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT HOLDER OR CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE OF THE PACKAGE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.