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Constructing a 50/50 Doubling-or-Loss Bet with Vanilla Options

Article Quant Q&A · Author: phdstudent
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Summary

The document asks whether vanilla calls and puts, across strikes and maturities, can be combined with their underlying assets to create a payoff with roughly equal chances of doubling the invested capital or losing it all. It distinguishes the desired all-or-nothing outcome from binary options and asks whether continuous trading would be necessary.

The text presents the problem but contains no answer, proposed option structure, pricing analysis, or evidence that the target probabilities and payoffs can be achieved. It therefore serves as a question about engineering a digital-style payoff from standard derivatives rather than as a trading strategy. Any assessment would depend on assumptions about the underlying price distribution, option prices, trading constraints, and how the bet is defined over time; these issues are not addressed in the document.

Key ideas

  • The question is whether vanilla calls and puts can approximate a bet that either doubles capital or loses the full investment.
  • The proposed construction may combine options with positions in the underlying asset.
  • The author asks whether continuous trading is required to create the desired payoff.
  • No strategy, derivation, probability calculation, or supporting evidence is provided.

Tags

OptionsDerivatives pricingRisk management
Full text
# Using vanilla options (calls and puts), any strike and any maturity, is it possible to create a 50% type bet


# Using vanilla options (calls and puts), any strike and any maturity, is it possible to create a 50% type bet












Imagine that one has access to vanilla options on several assets - think about long calls, long puts, short calls and short puts on a platform like robinhood.

Using derivatives and the underlyings is it possible to create a 50% type bet? Something along the lines of: With $\approx$ 50% probability one doubles the capital invested, with $\approx$ 50% probability one loses everything?

I know there are binary options out there ... but I am specifically wondering using vanilla options. Would this require continuous trading?

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.