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I got stuck in one exercise of binary options, it says that I have to consider a stock that does not pay dividends, the current price of the stock is 100, the volatility of it is 20%, the risk-free rate is 4%, consider that the option has a term of one year. Let S(1) be the price of the stock at the end of the contract. The option will pay 10 if 100 <S(1)<120. And it will pay 20 if S (1)> 120. It will pay 0 otherwise. Calculate the price of the option. Now I know that for the second part I will have to use a Cash or nothing call option for the price for I'm not sure what to use in the first part, I also asume that my strike price is 120, is it right? What can I do for the first part? Thanks

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    $\begingroup$ Isn't this the sum of two cash-or-nothing options, one struck at 100 and one struck at 120? $\endgroup$ – StackG Jan 25 at 21:31
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This is the sum of the folowing cash or nothing (also called digital or binary) options:

1-Call with strike 100 and paying 10.

2-Call with strike 120 and paying 10.

hope it helps!

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  • $\begingroup$ Remeber the Pricing formula using Black and Scholes $\begin{align} &\text{Cash-or-nothing call:}\quad c_{cn}=Be^{-rT}N(d_2),\\ &\text{Cash-or-nothing put:}\quad p_{cn}=Be^{-rT}N(-d_2),\\ &\text{Asset-or-nothing call:}\quad c_{an}=Se^{-qT}N(d_1),\\ &\text{Asset-or-nothing put:}\quad p_{an}=Se^{-qT}N(-d_1).\\ \end{align}$ $\endgroup$ – Alonso Rangel Jan 27 at 1:48

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