Is there a relationship between price of underlying and option premium?

Discussion in 'Options' started by 76132, Sep 20, 2011.

  1. 76132


    Ok, assume we have two options on two different underlying assets. Let's assume the time till expiration, implied volatility, interest rates, etc... are all the same. The only difference between the two options and underlyings are the strike price and price of the underlying.

    Let's assume the price of the first underlying is $1, and the price of the second underlying is $1000. The strike price of the options on the underlyings are so that:

    "strike price asset of 1"/"price of underlying 1" = "strike price of asset 2"/"price of underlying 2"

    In other words, the % of the strike price and the price of the underlying asset are the same for the two assets.

    What is the relationship between the price of the two options both when they are OTM and ITM? Is there a graph that shows this?

    On the top of my head, I'd expect the option premium on the $1 asset to always be lower than the premium on the $1000 asset. This makes sense when the options are ITM as the option on the $1000 asset will be much larger due to a larger intrinsic value. But what happens when the option is OTM? If the option price does not decline with a fall in the price of the underlying, then couldn't there be a point where it's not even worth buying the option? For example, if there was an asset worth 1 cent, it would not be worth it to buy the an option that costs 2 cents.

    What is the relationship between the price of the option and price of the underlying? Is there a ratio that describes this? What is the 'lower bound' for the price of the underlying? How does the transition between an ITM and OTM differ for options on underlyings with largely different prices? How does all this change as we tweak implied volatility, time to expiration, etc...

    Thanks. Sorry for the long post.
  2. Do you have access to Excel?
  3. 76132