Digital Option Pricing - Quant Researcher Interview Question

Problem Description

Digital options, or binary options, are exotic derivatives with discontinuous payoffs that depend on whether the underlying asset price satisfies a specific condition at maturity. These instruments are widely used in quantitative finance for hedging specific price levels and constructing complex payoff profiles. Pricing them under the Black-Scholes framework involves calculating the probability of the option expiring in-the-money, adjusted for risk-neutral valuation. Task Implement the function