Bounding an Out-of-the-Money Put from an At-the-Money Call

Summary

The document asks how to bound the price of an out-of-the-money vanilla put when the only readily observable option price is an at-the-money call. It notes two basic constraints: call-put parity and the fact that call prices decline as strike increases. The question seeks tighter bounds under model-independent or modest assumptions, reflecting a market where other strikes are illiquid or unavailable.

No proposed bound, derivation, assumptions, or market evidence is included, so the document is an open pricing question rather than a worked method. Any stronger estimate would depend on additional information or assumptions about the underlying distribution, volatility surface, rates, and carry. The text does not specify those inputs or indicate how reliable a resulting bound would be, so it cannot support a numerical price conclusion on its own.

Key ideas

• Put-call parity and the monotonicity of call prices provide basic constraints on option values.
• The question concerns a vanilla out-of-the-money put when only an at-the-money call price is observable.
• Tighter bounds would require additional market information or assumptions about the underlying and option prices.
• The document supplies no derivation, bound, or evidence to assess a proposed estimate.

Tags

# Model independent (or reasonable assumption) bounds on OTM put price given an ATM call price


# Model independent (or reasonable assumption) bounds on OTM put price given an ATM call price












I am looking for model independent (or weak/reasonable assumption) bounds on price of a OTM vanilla put on strike $k1$, conditional on an observable price for a ATM call at some strike $k2$. I understand I can use call put parity and the fact that calls are decreasing in strike, however I am looking for something stronger than that (with not too ridiculous assumptions of course). Any help is appreciated.

The context is that of a vanilla market which only has liquid observable prices of ATM calls but not much else.

Thanks!

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