# Does an option's price “ratio” with the underlying security price?

I'm trying to understand option pricing better.

Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then drops to \$30, should the price of a $28 PUT option with 40% implied volatility (and 90 days till expiration), now have a price of:  30 ----- * price of$38 PUT?
40


Similarly, do stocks at around \$100 / share, have options whose time value is twice as much as a stock trading at \$50 a share, everything else (e.g. volatility) being equal?

P.S. Another similar area of this question is selling covered calls. For the static return, one of course divides the sale price of the option against the cost of the underlying security, and one is often seeking to maximize that return. So, I guess one could say/ask, will a stock trading at \$40 a share, generate the same return ratio as a stock trading at \$30 a share, if those options have the same implied volatility?

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No, just apply the Black and Scholes formula to see the difference. –  Bob Jansen Nov 26 '11 at 16:52
there is reason to option pricing, and the parts that do not follow reason, just brush those aside as "volatility" and "slippage". you need to learn the reason part because a lot of your questions seem like you jumped in with some very specific instructions but no knowledge of the mechanics –  CQM Nov 28 '11 at 1:11

## 1 Answer

Almost. If you compare the price of a \$38 put option on a security worth \$40 and the price of a \$28.50 put option on a security worth \$30, then the price of the second option is indeed 3/4 of the price of the first option (assuming the other parameters are all the same).

The reason is that the unit of money does not matter. If the price of a put option with a strike of 38 dollars on a security worth 40 dollars is X dollars, then the price of a put option with a strike of 38 cents on a security worth 40 cents is X cents, and the price of a put option with a strike of 38 units of 0.75 dollar on a security worth 40 units of 0.75 dollar is X units of 0.75 dollar.

You can also see this from the Black-Scholes formula, but then you have to believe all the assumptions that are made in deriving the formula.

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