Math::Business::BlackScholes::Binaries
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%) );
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
USAGE my $price = vanilla_call($S, $K, $t, $r_q, $mu, $sigma) DESCRIPTION Price of a Vanilla Call
USAGE my $price = vanilla_put($S, $K, $t, $r_q, $mu, sigma) DESCRIPTION Price a standard Vanilla Put
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
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
returns the DS term common to many BlackScholes formulae.
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
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
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
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
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
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)
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)
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.
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.
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.
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.
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.
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.
* Math::CDF * Machine::Epsilon
https://github.com/binary-com/perl-math-business-blackscholes-binaries
[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
binary.com, <rohan at binary.com>
<rohan at binary.com>
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.
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You can find documentation for this module with the perldoc command.
perldoc Math::Business::BlackScholes::Binaries
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To install Math::Business::BlackScholes::Binaries, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::Business::BlackScholes::Binaries
CPAN shell
perl -MCPAN -e shell install Math::Business::BlackScholes::Binaries
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