Including Continuous Dividends in Longstaff–Schwartz American Call Pricing

Summary

The document asks how a continuous dividend yield should be incorporated when applying the Longstaff–Schwartz least-squares Monte Carlo method to price an American call. The author expects the dividend yield to affect simulated geometric Brownian motion paths and asks whether it changes any other part of the method compared with the non-dividend-paying case.

No answer, derivation, implementation, or numerical evidence is included. The question identifies two parts of the problem that a complete treatment would need to address: the effect of dividends on the risk-neutral stock dynamics and the continuation-versus-exercise comparison at each exercise date. It does not establish whether changing the simulated paths alone is sufficient. The document is therefore useful as a narrowly framed pricing question, but it is not a worked guide to dividend-aware LSM implementation, and readers would need additional material to resolve the modeling details.

Key ideas

• The document asks how continuous dividends enter Longstaff–Schwartz Monte Carlo pricing of American calls.
• It identifies simulated stock paths as one place where the dividend yield may matter.
• It also asks whether other steps differ from the non-dividend-paying case.
• No solution, derivation, or pricing evidence is provided.

Tags

# LSM American Option pricing with dividends


# LSM American Option pricing with dividends












Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying GBM stock paths but is there anywhere else where it differs from the LSM on a non-dividend paying stock?

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