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Is it possible to create a synthetic long single stock future using the stock and it's vanilla options with the caveat that selling naked puts is NOT allowed? That is, you can write puts, but they must be cash-secured for 100% of the potential loss. This implies that a long-call short-put combo is not allowed.

If this is possible, how do you do it?

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If you mean, write a put and buy the stock, pretty sure the answer is no. If the stock price tanks, well below the strike, you will have lost twice (on the stock and the put). Ie, your delta will be 2, not 1 like a future. On the upside, the delta will be 1, plus the premium, again not the same as a future.

Similarly, your vega will not be zero as it is for the future.

But even the long-call short-put combo doesn't replicate a future's cash flows unless you have daily settlement of the options mark to market.

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