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i have two questions which are simple i think.

  1. Is it possible for a call option to be issued on the market with a strike price higher than the underlying asset's current price?

  2. In a market without arbitrage opportunities, we know that there is the Call/Put parity which is given by the formula C(t)-P(t)=S(t)-K*exp(-r(T-t)). However, to estimate the price of a call, we have the following formula. This formula also works for the price of a put. However, the price of a call and a put is not the same according to the call/put parity. I don't understand why both prices are approximated by the same formula: $0.4*S*\sigma*\sqrt(T)$

Thank you in advance for your answers

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    $\begingroup$ "we have the following formula". What is it ? I think you omitted the formula. $\endgroup$
    – nbbo2
    Dec 17, 2023 at 16:17
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    $\begingroup$ With regards to strike price; do you know you can just look up options on the exchanges website? $\endgroup$
    – AKdemy
    Dec 17, 2023 at 16:38
  • $\begingroup$ If you look at price tables: For a high strike the Call price is smaller than the Put price, for a low strike the Call price is bigger than the Put price => by continuity, somewhere in the middle the Call price will be approx equal to the Put price. In that middle range it may indeed be possible to approximate P or C by the same expression (But it is a special case. The Put Call Parity is perfectly general). $\endgroup$
    – nbbo2
    Dec 17, 2023 at 16:51
  • $\begingroup$ @nbbo2 yes sorry i forgot it. When you say "for a high strike" it's compared with the underlying asset price, right ? So the formula to approximate both are right at the money. $\endgroup$ Dec 17, 2023 at 18:19
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    $\begingroup$ Yes, the approximation formula is only valid for $K \approx S e^{r(T-t)}$ (or $K \approx S$ for $r=0$). There are usually many available $K>S$ and many $K<S$ options in the market place. $\endgroup$
    – nbbo2
    Dec 17, 2023 at 19:32

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