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Compute the prices of European Binary call or put options according to
Reiner and Rubinstein (Unscrambling the Binary Code, RISK 4 (October 1991),
pp. 75-83) valuation formulas:
Option type Gap
A gap call option pays the difference (gap) between spot and either one of two
strike values:
C(S,X1,X2,T) = X2*exp(-rT)*N(d) P(S,X1,X2,T) = X2*exp(-rT)*N(-d) d = (log(S/X1) + (r - divrate + 0.5*sigma^2)*T)/(sigma*sqrt(T))
Option type Cash-or-Nothing
A cash or nothing option pays the pre-defined amount X2 if the value is larger
than the strike X1 (call option) or lower than the strike X1(put option):
C(S,X1,X2,T) = N(d)*X2*exp(-rT) P(S,X1,X2,T) = N(-d)*X2*exp(-rT) d = (log(S/X1) + (r - divrate - 0.5*sigma^2)*T)/(sigma*sqrt(T))
Option type Asset-or-Nothing
An asset or nothing option pays the future spot value S if the value is larger
than the strike X1(call option) or lower than the strike X1 (put option):
C(S,X1,T) = S*N(d)*exp(-divrate*T) P(S,X1,T) = S*N(-d)*exp(-divrate*T) d = (log(S/X1) + (r - divrate + 0.5*sigma^2)*T)/(sigma*sqrt(T))
Option type Supershare
A supershare option has a payoff, if the future spot values lies between
an lower bound X1 and upper bound X2, and is zero otherwise:
Value(S,X1,X2,T) = (S*exp(-divrate*T)/X1) * (N(d1) - N(d2)) d1 = (log(S/X1) + (r - divrate + 0.5*sigma^2)*T)/(sigma*sqrt(T)) d2 = (log(S/X2) + (r - divrate + 0.5*sigma^2)*T)/(sigma*sqrt(T))
All formulas are taken from Haug, Complete Guide to Option Pricing Formulas,
2nd edition, page 174ff.
Variables:
See also: option_willowtree, option_bs.
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