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QUESTION

Recalculate the initial premiums if the options of question 1 are
binary options which pay

$$\mathit{payoff}(S_r)=\left\{\begin{array}{cc}\$1,&S_r\geq
K\\o,&S_r<K\end{array}\right.$$


ANSWER

Binary formulae are:

Call$=e^{-r(T-t)}N(d_2)$

Put$=e^{-r(T-t)}(1-N(d_2))$

Use data of question 1 at $t=0$: $d_2=-0.7271, N(d_2)=0.2327$

Therefore call price at $t=0=e^{-0.05}\times0.2327=0.2214$

put price at $t=0=e^{-0.05}\times(1-0.2327)=0.7299$




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