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Why Stock and Option Positions Do Not Replicate a Single-Stock Future

Article Quant Q&A · Author: cona
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Summary

The document asks whether stock and vanilla option positions can create a synthetic long single-stock future when short puts must be fully cash-secured. It considers buying the stock and writing a put as a possible substitute, while noting the familiar long-call, short-put combination is unavailable under the stated constraint.

The answer explains that buying stock and writing a put does not produce a futures-like payoff: below the put strike, losses accrue both on the stock and through the short put, making the position’s sensitivity differ from that of a future. The position also has nonzero vega, whereas the answer treats the future’s vega as zero. Even a long-call, short-put combination does not match futures cash flows unless option positions are marked to market and settled daily. The reply is brief and does not quantify contract terms, financing, dividends, or alternative structures, so it offers a payoff-level warning rather than a complete replication analysis.

Key ideas

  • Buying a stock and writing a put can create greater downside exposure than a long future.
  • The stock-plus-short-put position has delta that changes with the stock price and put moneyness.
  • The proposed stock-and-put position carries volatility exposure, unlike the future described in the answer.
  • A long-call, short-put combination does not match futures cash flows without daily mark-to-market settlement.

Tags

EquitiesOptionsFuturesDerivatives pricing
Full text
# Create a Synthetic Single Stock Future


# Create a Synthetic Single Stock Future












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?

## Answer by ThatDataGuy (score 1)

https://quant.stackexchange.com/a/53482

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.

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.