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Call Prices Decline as Strike Prices Rise

Article Quant Q&A · Author: TmSmth
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Summary

The document addresses how to price a call option with a strike above $100 when the call struck at $100 is known to cost $2.97. The accepted reply applies the standard monotonicity relationship for calls with the same underlying and expiration: raising the strike cannot increase the call’s value. Therefore, the higher-strike call must be worth less than the cited lower-strike call.

This gives a simple no-arbitrage bound that can help check an option-price estimate. It does not calculate the higher-strike call’s exact price or rely on a risk-neutral probability calculation. The conclusion depends on comparing otherwise matching calls, and the brief exchange supplies no additional details about the underlying, maturity, rates, dividends, or market conditions. It is a useful pricing constraint, rather than a complete valuation method.

Key ideas

  • For otherwise matching calls, a higher strike cannot have a higher price than a lower strike.
  • The stated $2.97 price for the call struck at $100 bounds the price of calls with higher strikes.
  • Strike monotonicity provides a no-arbitrage check, but it does not determine an exact option value.

Tags

OptionsDerivatives pricing
Full text
# Call price in case of AOA


# Call price in case of AOA












I have this exercice, and for the last question, i tried to say that with lower bound, $C > S_0 - Ke^{-rT}$ which is $-8$ something but it doesn't make sense so i don't know what to do. Could we just say that under risk-neutral probabilities, price of call is $0.5*5*e^{-rT}$ , as $S_0$ should be the expected value of $110$ and $90$ in $t_1$ with $p = 0.5$ for example ?

## Answer by Canardini (score 3, accepted)

https://quant.stackexchange.com/a/49968

A call struck at $100$ costs $2.97$, therefore a call with a strike higher than $100$ must cost less than $2.97$.

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.