Comparing Option Richness with Implied Volatility and Expected Value

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


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












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 by KaiSqDist (score 1)

https://quant.stackexchange.com/a/78858

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 by Arshdeep (score 1)

https://quant.stackexchange.com/a/78859

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.

## Answer by Dr. Michael J. Stefano (score 1)

https://quant.stackexchange.com/a/85339

maybe this is simpler and more practical:

the 8 option: 8/7 = 1.14 making that option 14% overvalued compared to the theo value

the 6 option: 6.75/6 = 1.12 making that option 12% overvalued.

BUT

now what you also need is expected value, so if you had the deltas, we could use them to estimate probabilities and expected value(EV).

for instance, if these were overpriced calls, and you were deciding whether to sell the $8 call at say a delta of .30 or the $6.75 call at a delta of say .25, then you could do this math:

we will estimate the likelihood of the $8 call with a .30 delta expiring worthless in your favor at 70% based on the .30 delta. therefore its expected value would be $8*.7 = 5.6

similarly for the $6.75 call with a delta of.25, the EV would be 6.75*.75 = 5.06.

now you have a way to compare them both, and that is EV using deltas as estimates of probability.

so the initial calc showing which one was more overpriced wasnt the most important factor, in this example.

and the fact that the further OTM call for $6.75 had a higher IV also didnt matter, in this example.

now these arent the real deltas but this is how you could do it.

also you can see that if you wanted to sell a call credit spread, that based on the theo value that you should collect $1, but the actual prices give you a net credit of 1.25, which is 25% higher than the theo value, based on historical volatility.

so the increased IV across the strike skew is making this trade more profitable at the moment than it might have been prior to the increase in IV and therefore the hope is that the IV will mean revert backdown to the realized volatility and not the other way around, where the IV is predicting a higher realized volatility that comes to bear before expiration.

i hope this helps.