Critical Stock Price in the Geske Compound-Option Formula

Summary

The document introduces the critical stock price used in the Black–Scholes formula for pricing compound options, following Geske. It defines this threshold as the stock price at the compound option’s expiration that leaves the underlying option at the money. The question asks whether the formula’s dependence on this threshold means Monte Carlo simulation is needed to evaluate the price.

The excerpt does not provide an answer or a pricing procedure. It therefore offers a useful definition and identifies a computational question, but it does not establish that simulation is required or explain how to find the critical price. Readers should treat the Monte Carlo claim as an open question in this document, rather than as a conclusion. No numerical example, validation, or discussion of solution methods is supplied.

Key ideas

• The Geske compound-option formula includes a critical stock-price threshold.
• The threshold is defined by the underlying option being at the money at the compound option’s expiration.
• The document asks whether determining this threshold requires Monte Carlo simulation.
• No answer or numerical method for evaluating the threshold is provided.

Tags

# Determination of critical stock price in compound option pricing


# Determination of critical stock price in compound option pricing












Under the Black-Scholes framework, there is a closed form formula for the price of a compound options, as first derived by Geske (1979). However, the analytical formula refers to a critical stock price, which is the value of the stock at expiration date of the compound option such that the (underlying) option is at the money at the expiration date of the compound option.

Just to confirm: even though the formula for the compound option is "analytical", the evaluation of it still requires Monte Carlo as the critical stock price is not known in advance (at the time of pricing), is this correct?

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