# Option pricing within the Black Scholes model

Have a question regarding regular option pricing.

In the standard Black-Scholes model, with interest r and volatility $\sigma$. Determine the arbitrage free price at t of an option which at $T>t$ pays the holder the amount of 100 USD dollar if the stock price is between 50 and 100 USD. I.e. option with pricing function:

$\phi = 100$ if $50<S_T<100$ else nothing.

A thorough walk through in how to calculate this price would be highly appreciated.

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