Calculating Black-Scholes Delta for Barrier Options

Summary

The document asks how to calculate the Black-Scholes delta of a knock-in or knock-out barrier option. It lists the inputs the questioner has available, including barrier and strike levels, spot price, time to expiry, option type, implied volatility, and the risk-free rate, and contrasts the problem with the familiar delta formula for a vanilla call.

No barrier-option formula or explanation is provided in the document. The answer would depend on contract details such as barrier direction and monitoring conventions, which are not specified. As presented, this is an open derivatives-pricing question rather than a worked method, and it offers no numerical example or evidence to validate an approach.

Key ideas

• Barrier-option delta depends on whether the contract is knock-in or knock-out.
• The question supplies spot, strike, barrier, expiry, volatility, rate, and call-or-put type as inputs.
• Vanilla call delta is offered as a reference point, but no barrier formula is given.
• Contract details beyond the listed inputs may be needed to determine the appropriate delta.

Tags

# Black-Scholes delta of a barrier (knock-out or knock-in) option


# Black-Scholes delta of a barrier (knock-out or knock-in) option












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

- Whether it is knock-out or knock-in

- Barrier price

- Strike price, $X$

- Current stock price, $S$

- Number of days to expiry, $\tau$

- Whether it is a call or a put

- Implied volatility, $\sigma$

- Risk-free rate, $r$



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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