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I'm trying to calculate the Black-Scholes delta of a barrier option given the following information:

  1. Whether it is knock-out or knock-in
  2. Barrier price
  3. Strike price, $X$
  4. Current stock price, $S$
  5. Number of days to expiry, $\tau$
  6. Whether it is a call or a put
  7. Implied volatility, $\sigma$
  8. Risk-free rate, $r$
  9. Note: there is 0 dividend yield

I know the formula for the delta of a basic call option is the following: $$N(d_1)\text{ where}$$ $$d_1 = \frac{ln(S/X)+(r+\sigma^2/2)\tau}{\sigma\sqrt{\tau}}$$

Is there a similar formula for a barrier option?

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