Inputs for Pricing a Down-and-Out Call in Black–Scholes

Summary

The document asks how to price a down-and-out call in a Black–Scholes setting. It specifies a strike and barrier at the same level, a spot price above them, zero interest rate, and a stated volatility. The request seeks a simple formula or proxy for this barrier option. A down-and-out call is path-dependent: its payoff depends not only on the terminal underlying price but also on whether the price has crossed the lower barrier during the option’s life.

No solution, option maturity, derivation, or numerical price is provided in the document. In particular, maturity is needed to calculate a Black–Scholes barrier-option value, so the stated inputs do not determine a unique price. The question is useful as a pricing problem, but the text supplies neither evidence nor a method to assess; any valuation would require additional contract details and a specified pricing formula or approximation.

Key ideas

• A down-and-out call depends on whether the underlying crosses its lower barrier before expiry.
• The document specifies strike, barrier, spot, interest rate, and volatility as pricing inputs.
• It asks for a formula or proxy but provides no pricing method or result.
• Option maturity is absent, so the stated inputs are insufficient to determine a unique value.

Tags

# Price of barriers in black scholes


# Price of barriers in black scholes












Do you know a simple way or proxy, formula to determine the price of a down and out call with strike 100, barrier 100, spot 110 in a BS world with no rate and a 10% vol ? Thanks for your help

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.