Risk-Neutral Stock Path Generation for American Option Simulation

Summary

The document asks how to recreate the stock price paths used in a numerical example from Longstaff and Schwartz’s simulation-based treatment of American option valuation. The author understands the broad purpose of the example but wants the assumptions and steps needed to generate the paths under the risk-neutral measure. This points to a useful modeling question: option valuation simulations require a specified risk-neutral price process and inputs, then simulated paths sampled from that process.

The document itself does not provide those assumptions, a path-generation method, parameter values, or a worked calculation. It is a request for an explanation and references, so it offers no numerical evidence or comparison of approaches. Readers should treat it as identifying a gap in reproducing the example rather than as a complete guide to Monte Carlo pricing. In particular, it does not establish which model or discretization the cited example uses.

Key ideas

• The author seeks to reproduce stock paths in a numerical American option pricing example.
• The paths are described as being generated under a risk-neutral measure.
• The document gives no model specification, inputs, simulation steps, or results.

Tags

# Generating process for stock price paths in this paper?


# Generating process for stock price paths in this paper?












I am reading Longstaff and Schwartz Valuing Aerican Options by Simulation because monte carlo simulations, especially their use in option pricing, is interesting to me. However, I am having some difficulty getting through the numerical example - not from lack of understanding the big picture but recreating the example myself.

On page 116 the authors discuss stock price paths - they say they are generated under the risk neutral measure but I am missing some background here that will allow me create this example on my own for understanding (or a different example for me to work through). I feel that the authors left out some critical information here on exactly how this example was produced.

Can anyone explain to me how these stock prices are generated, or link me to resources so I can figure it out myself? It would go a long way towards me fully understanding this paper.

Thank you!

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