Why Option Writers Charge Fair Value and Hedge Their Exposure

Summary

The document addresses why a bank would sell an option when a favorable move in the underlying could make the payout larger than the premium collected. The example assumes a call premium of five dollars and a later stock price of one hundred ten dollars, but the response points out that the assumed premium is not a fair value for the described deep in-the-money call. A fair option price reflects the probability distribution of possible outcomes, along with relevant pricing factors, rather than just the payout in one realized scenario.

The response also explains that a bank may sell an option to offset an existing position, such as hedging a short call with a long call. Thus, an option sale can be priced to compensate for expected risk or serve a broader portfolio purpose; the seller is not necessarily making an unhedged directional bet. The brief exchange offers no detailed pricing model, hedge strategy, or discussion of market-making costs, so it introduces the intuition without establishing a complete account of dealer economics.

Key ideas

• An option’s fair premium reflects the range and likelihood of possible outcomes, not one eventual price path.
• The example’s assumed premium is too low for the described in-the-money call, according to the response.
• Banks may write options to hedge other positions in their portfolios.
• An option seller’s realized profit depends on pricing and the outcome, not simply on the premium received.

Tags

# Why do banks offer options?


# Why do banks offer options?












I have only taken one introduction class in finance. However we came along opinions, their pricing, etc. We only contemplated being the buyer of a option. If everything works for you apparently you can earn a high yield. Thus I'm wondering why a bank (or another institution) would offer options. Say there's a stock which costs \$100. The bank offers a (European) call with a striking price of \$95, so you'll pay \$5 for the option (I know there're other factors which determine the price but want to neglect them here to keep it simple). After a certain amount of time the option matures while the stock is at \$110. The bank owes you \$15 (in case of cash settlement which should be the default case in the real world). They sold it for only $5 though and lost money.

So, why would a bank issue the option at all? One may argue because they expect the stock to fall but often they do offer both put and call options and on the put option they would only earn what they can sell it for in this case.

## Answer by phdstudent (score 5)

https://quant.stackexchange.com/a/22245

You are neglecting several other things. (1) That deep in the money option is worth far more than 5 USD. (2) The fair price will actually take into account the probability that the stock will rise to $110 at maturity. (3) Also the bank might be hedging some other positions, such as a short call with that long call.

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.