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Pricing an American Put with a Floating Strike

Article Quant Q&A · Author: Anna Taurogenireva
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Summary

The document poses a pricing question for an American put on a non-dividend-paying stock. Its strike declines over time at the risk-free rate, and the stock is assumed to have constant volatility. This setup makes the contract different from a standard fixed-strike American put and calls for accounting for the changing exercise value.

The only suggested approach is to express the option value as intrinsic value plus an early-exercise premium, with an external reference offered for further detail. The document does not derive a formula, explain how to calculate the premium, or provide numerical examples or pricing evidence. As a result, it identifies a useful decomposition but is too brief to establish a complete valuation method; readers would need the referenced material or additional modeling assumptions to obtain a price.

Key ideas

  • The option is an American put whose strike declines at the risk-free rate as maturity approaches.
  • The underlying is assumed to pay no dividends and have constant volatility.
  • The proposed valuation separates intrinsic value from an early-exercise premium.
  • The document gives no derivation or calculation procedure for the premium.

Tags

OptionsDerivatives pricingVolatility
Full text
# Pricing American with floating strike


# Pricing American with floating strike












Consider a American floating strike put option with maturity $T$, written on a non-dividend paying stock $S_t$. The strike of this option at time $t\leq T$ is $Ke^{-r (T-t )}$, where $r$ is the constant interest rate.

Assume the volatility of the underlying stock is constant.

What is the price of this option?

## Answer by emcor (score 5)

https://quant.stackexchange.com/a/14882

These options can be priced by adding an early exercise premium value to the intrinsic value:

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.542.3141&rep=rep1&type=pdf

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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