One of most challenging problems from applying the Black-Scholes model to financial derivatives, is reconciling the deviation between the expected and observed values. This study derives an extension of the Black-Scholes model and recovers the real drift of binary call options from their market prices. For space-dependent real drift, we obtain stable linearization and an integral equation. We also find that using market prices of options with different strike prices enables us to identify the

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... rm structure of the real drift. Results demonstrate that our new approach can confirm the existence of arbitrage opportunities in a binary option transaction.