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Pricing a Perpetual American Put with Zero Volatility and No Dividends

Article Quant Q&A · Author: Anirban Saha
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Summary

The document asks how to value a perpetual American put under simplified assumptions: a positive interest rate, zero volatility, and no dividends. It identifies the strike and interest rate as the relevant inputs and acknowledges that pricing involves determining an optimal exercise boundary. The question is framed as a request for a derivation or explanation, rather than presenting a proposed formula or binomial-tree calculation.

No answer, numerical example, or method for finding the boundary is included. Consequently, the document provides no evidence for a particular price and does not explain whether or how a binomial tree handles the zero-volatility limit for a perpetual contract. It is useful as a focused problem statement about early exercise and optimal stopping under restrictive assumptions, but a reader needs additional derivation to learn the actual valuation procedure. The assumptions make it a special case and do not address how volatility, dividends, or finite maturity would affect the result.

Key ideas

  • The question concerns a perpetual American put with positive interest and zero volatility and dividends.
  • The strike and interest rate are identified as inputs to the valuation problem.
  • The author recognizes that an optimal exercise boundary is relevant.
  • No pricing derivation, answer, or binomial-tree procedure is supplied.

Tags

OptionsDerivatives pricingRisk management
Full text
# How to price a Perpetual American Put Option with the Binomial Tree Model?


# How to price a Perpetual American Put Option with the Binomial Tree Model?












How do we price an American Put Option with simplified assumptions of non-zero interest rate but zero volatility and zero dividend rate?

I understand the concept of Perpetual American Options and I know we need to find optimal boundary constraints. But I fail to understand how we can price the Perpetual American Put Option with an interest rate (say) `r` and strike price (say) `K`.

Any notes/ answer would be helpful!

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