How to conclude which option is overpriced (by using implied volatility)

Question

I have a small question regarding how to conclude which option is more overpriced?

See the following table

Option Theoretical Value	Option Price	Option Implied Volatility
7.00	8.00	26%
6.00	6.75	28%

Here, we are given theoretical option price the volatility used for this is 23%. Since both options are overpriced, their implied volatility is higher than 23%. Given the implied volatilities of both options, How can a option trader conclude which is more overpriced among these two, so that he could profit by buying/selling the spread?

Answer 1

Are these options priced with Black-Scholes or some other model? Most often, models assume a risk-neutral framework to simplify the pricing of these products and do not consider the risk preferences of investors.

If the observed market prices of options you quoted are liquidly traded, they could be "fairly" priced while accounting for the risk preferences of investors.

I feel to consider if an option is undervalued or overvalued is not such a straightforward issue... maybe an options expert can weigh in.

Answer 2

If 23% vol is going to be really the realised vol, then both are overpriced and delta hedging both will give you a positive PnL.

If you calculate delta with realised vol, you gain the difference in the prices, which is vega times error in implied vol. From here, you can choose whichever option has a higher yield.

If you calculate delta with implied vol, you gain gamma weighed difference between implied and realised vol. This is non deterministic over life of the option and what you end up with depends on the path.