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Option Delta Hedging, Dealer Spreads, and Real-World Hedge Risk

Article Quant Q&A · Author: mowgli
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Summary

The document explains why a delta-hedged option position is not necessarily a source of trading profit. In an idealized model, a perfectly hedged portfolio earns only the risk-free rate. A dealer may earn revenue by selling an option above its theoretical value or repurchasing it below that value, while hedging away much of the option’s subsequent exposure.

A trader could also profit from having a better volatility estimate than the market, though the response cautions that doing so consistently is difficult. In practice, continuous rebalancing is impossible and trading costs affect returns, so a delta hedge leaves residual gains or losses. The exchange is a qualitative explanation rather than a detailed pricing or hedging analysis; it does not quantify spreads, costs, or hedge error.

Key ideas

  • An ideal perfectly hedged option position earns the risk-free rate in the model described.
  • A dealer can seek profit from the spread between an option's sale price and its theoretical value.
  • A superior volatility estimate may create an opportunity, but consistent forecasting is difficult.
  • Discrete hedge adjustments and trading costs leave real-world delta hedges imperfect.

Tags

OptionsDerivatives pricingVolatilityExecution
Full text
# Why/How does a hedged portfolio make profits?


# Why/How does a hedged portfolio make profits?












This is probably a very easy question but I am new to the field and couldn't find an answer.

Assuming that I am building a hedged portfolio with a long option and going short delta on the underlying. Then, if I understood correctly tomorrow's value of the portfolio will be the same as today's. (Please correct if this is a wrong understanding.)

My question is: If tomorrow's value is the same as today's (and by extension the day after tomorrow and so on until the option expires) how does this strategy make profits?

Thank you

## Answer by Alex C (score 4)

https://quant.stackexchange.com/a/18341

An Investment Bank earns a profit by selling you an option at a slightly higher price than the theoretical price, or buying it back from you at a slightly lower price. They call this "earning a spread". Then they hedge the option, so as not to make any [further] gains or losses on it (other than the risk free rate).

Another way they could earn a profit is if they have a more accurate estimate of volatility than other people have. But that is not easy to do consistently.

## Answer by Stefan Voigt (score 1)

https://quant.stackexchange.com/a/18342

A perfectly hedged portfolio should not make any profits different from the risk free interest rate. However, you won't be able to hedge perfectly in the real world. Delta hedging for example requires continous trading and adjusting (this is one way to derive the black -scholes formula: thex hedge the stock perfectly and therefore obtain a risk -free rate deterministic return) - continous trading can not be realized. Furthermore trading costs will distort your return. Therefore, you will not obtain a perfect hedge and leave room for making profits (and loses )

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.