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Is there any way to simulate buy an option at a pric of x when that price is not available to buy ? If x-3 and x+3 exists, how do I buy it at price x?

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    $\begingroup$ You could buy a half position in the X-3 option and another half position in the X+3, but of course it would only be an approximation to the position you want, not an exact replica. $\endgroup$
    – noob2
    Jul 28 '20 at 23:46
  • $\begingroup$ Agree . I was thinking if there are ways to get closer to it than just trying to buy half. Given a delta is there any way to find the options to buy to get that value? $\endgroup$
    – roller
    Jul 28 '20 at 23:58
  • $\begingroup$ I don't grasp why you would want to buy at price X. Now if you were asking if buying a strike of X-3 and a strike of X+3 would simulate buying a strike of X then I would say yes with it being more so (over the short term) if the underlying is trading at/near X. $\endgroup$ Aug 16 '20 at 19:38
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With option pricing, at least with BSM model, you can observe every input except for implied volatility. So all you need to do is provide an implied volatility into your pricing model and your custom strike price to produce an option price. With that IV assumption, you can produce all the greeks you need according to BSM model.

If X-3 and X+3 are not that far from X (you'll have to use your judgement), you can expect that the IV of X to be in between the other two. IV also tends to be in between the two if X-3 and X+3 are at one end of the skew. Note that in practice, there may be cases where the IV of the middle option is not in between the two outer options, especially when you get close to ATM. However, the amount the IV of the middle option differs from the outer options has a bound (it cannot be so where the middle option is worth less or greater than both the outside options, with negligible adjustment for interest rates). Even if skew exists, you can still back into an approximate option price as long as you can supply an IV figure.

All the above is under the assumption you are talking about plain vanilla options and options on stuff like equity or commodity futures.

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