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How Put-Side Skew Changes Vertical Spread Payoffs

Article Quant Q&A · Author: abdulrahman alothman
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Summary

The document asks whether an at-the-money SPX put spread has an edge over a same-width call spread because the put spread's stated reward-to-premium ratio is higher. It frames the comparison as a roulette game with different payouts but supposedly equal odds.

The reply challenges the assumption that the spreads have equal probabilities. Option prices reflect market-implied probabilities, which need not match a trader's subjective view. A trader who believes the odds are mispriced can express that view by trading, but the payoff ratio alone does not establish an edge. The exchange offers no data, model, or empirical test to determine whether either spread is attractive; it only clarifies that the probability premise is an opinion rather than an objective fact.

Key ideas

  • A higher potential payoff on a put spread does not by itself prove that it has positive expected value.
  • Market-implied probabilities for put and call spreads need not be equal.
  • A trader may take a position when their probability estimate differs from the market's pricing.

Tags

OptionsDerivatives pricingUS markets
Full text
# How skew in vertical put spreads change the payoff?


# How skew in vertical put spreads change the payoff?












An spx four strikes wide Put Spread from at the money has a payoff ratio of 1 to 2 meaning if the Premium on the spread is \$10 your reward is \$20; yet the corresponding Call Spread with the same width from at the money have a payoff ratio of 1:1 and I know it's because of the skew on the put (downward) side.

But both have the same probability, it's like a Roulette table that pay 2:1 on black and 1:1 on red. So my question isn't this an edge for any one taking the Put Spread?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/41458

Well, the probabilities implied by the market are not equal. If you believe they should be equal, then go ahead and express yourself in the market. The point is , it is not an objective fact that it must be 50/50- that's your subjective opinion.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.