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Good day, I wanted to ask for help with a question from one of my exercise sheets.

For a share S the market quotes a given strike K in both european and american styles. Use an arbitrage argument to construct a formula relating the price of the european call option to the price of an american call option.

I do not understand what is meant by EU and US style Market quotes. From my research, it just seems that

  • EU is quoted at K USD per share
  • US is quoted at $\frac{1}{K}$ shares per 1 USD

But this does not tell me much about applying an arbitrage argument. I have no idea about the formula that relates the two styles.

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    $\begingroup$ I think they mean European = exerciseable at maturity only. American = exerciseable at any time up till maturity. $\endgroup$ – dm63 Jan 22 '19 at 13:49
  • $\begingroup$ @dm63 Having said that, what would the formula then be? If we assume some sort of interest rate and apply it to the strike K, would that help in answering the question? $\endgroup$ – ʎpoqou Jan 22 '19 at 14:00
  • $\begingroup$ Your question seems to be missing some words. Perhaps you meant "construct a formula relating the price of the european call option to the price of an american call option" ? $\endgroup$ – Antoine Conze Jan 22 '19 at 14:45
  • $\begingroup$ Hint: If European options can only be exercised at maturity, and American options can be exercised any time including at maturity, which options would have more value? $\endgroup$ – AlRacoon Jan 22 '19 at 14:45
  • $\begingroup$ I would assume the US ones would have more value. $\endgroup$ – ʎpoqou Jan 22 '19 at 14:48