Short Straddle Returns Under Black–Scholes Assumptions

Summary

The document asks how much a short straddle could earn in the long run under an efficient market and Black–Scholes assumptions. It assumes the implied volatility used to price options matches future realized volatility, which remains constant over the holding period. It then suggests that selling both a call and a put at the same strike might produce returns above a risk-free rate because the position contains two options.

The text offers no derivation, numerical estimate, or supporting evidence for that conclusion. Its claim about doubling implied volatility does not establish that the straddle earns excess return: option prices and risk depend on payoff structure, capital requirements, and exposure to large moves. The assumptions also exclude transaction costs and other real-world frictions. Treat the question as an invitation to analyze the model, not as a demonstrated return result.

Key ideas

• The setup assumes an efficient market and the Black–Scholes framework.
• It equates implied volatility with constant future realized volatility.
• The document proposes, but does not demonstrate, that selling both options can earn more than a risk-free return.
• It provides no derivation or evidence for a long-run return estimate.

Tags

# Theoretical returns of Short Straddle in an efficient Options Market


# Theoretical returns of Short Straddle in an efficient Options Market












Assumptions:

- Market is efficient

- All assumptions of BS Model apply

- Implied Volatility predicted using BS model is same as actual volatility in future. Needless to say that the volatility is constant throughout the position period.

Description:

In BS model, option seller of a single strike itself makes a risk free return in the long run. Since in Short stradddle, two options are sold at same strike, the IV of the portfolio would be double that of actual volatility experienced in market. This implies that short straddle sellers can make more money than risk free return in the long run.

Question: By theory how much a short straddle seller can make in the long run?

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