Welcome to THETAWIKI. If you like to create or edit a page please make sure to login or register an account. All registered users please make sure to provide a valid email address.
Barrier Option
From ThetaWiki
There are numerous different Barrier options. The following code prices an up-and-out barrier option with barrier level H.
P = 100; sigma = 0.4; r = 0.05; t = 0; T = 2; H = 120; X = 100; d_1 = (log(P/X)+(r+0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_2 = (log(P/X)+(r-0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_3 = (log(P/H)+(r+0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_4 = (log(P/H)+(r-0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_5 = (log(P/H)-(r-0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_6 = (log(P/H)-(r+0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_7 = (log(P*X/(H^2))-(r-0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); d_8 = (log(P*X/(H^2))-(r+0.5*sigma^2)*(T-t) ) /(sigma*sqrt(T-t) ); a=(H/P)^(-1+2*r/(sigma^2)); b=(H/P)^( 1+2*r/(sigma^2)); V = P*(normcdf(d_1) - normcdf(d_3) - b*(normcdf(d_6)- normcdf(d_8)))... - X*exp(-r*(T-t))*(normcdf(d_2)-normcdf(d_4)-a*(normcdf(d_5)-normcdf(d_7)))
