Confused about Some Options Pricing

Discussion in 'Options' started by Wet, Sep 19, 2001.

  1. Wet


    All you Options Experts (def, zboy, others),

    I'm confused about some aspects of options pricing. Here's what I am confused about, using AMD as an example. Current price on AMD as I write is 9.70.

    The Jan 2002 10 calls (OTM) have a bid/ask of 1.75/2.00. As always, let's just assume the ask price. So these calls cost me 200 bucks a contract.

    The Jan 2002 7.50 calls (ITM) have an ask price of 3.30. Since the current AMD price is 9.70, the "price" of the call is really 110 a contract, since they have 220 dollars worth of intrinsic value.

    The Jan 2002 5 calls (deep ITM) have an ask at 5.10. So the "price" of the call is 50 bucks, since they have an intrinsic value of 460.

    Okay, here's my confusion. Obviously all of these calls expire at the same time. Everything is the same about them except that they have different strikes -- some are OTM, some are ITM, and some are deeper ITM.

    Why -- in the case of the Jan 7.50 and Jan 5.00 ITM calls -- is the time value different? After intrinsic value is deducted, the 7.50's have a time value of 110, and the 5.00's have a time value of 50.
    Shouldn't they be the same? I'm confused as to why they are different.

    Obviously, the 5.00 calls cost more than the 7.50's upfront. But it seems like it is a good idea to simply buy the more expensive options, since they are actually WORTH more.

    Is the reason the 5.00 calls "cost less" (after intrinsic value is removed) because I have risked more money "up front"?

    Any clarity here is appreciated.

  2. Put / Call parity!

    Options pricing is all about portfolio replication. Let's look at your example of AMD:

    Stock price = 9.70

    Strike Call
    10.0 2.00
    7.5 3.30
    5.0 5.10

    All the corresponding puts must have a value that does not allow an arbitrage. An option's premium is composed of intrinsic and time value. For the 10.0 Call, the intrinsic value is 0.30 and the time value is 1.70. For the 10.0 put, the intrinsic value is zero but there must be time value. To prevent an arbitrage, the price of the put must be 1.70 (or less).

    An example of a risk-free arb (let's assume we can buy or sell at the prices listed):

    Stock = 9.70 10 Call = 2.00 10 Put = 1.85

    If I sell 10000 shares at 9.70, buy 100 10 Calls at 2.00 and sell 100 10 Puts at 1.85 at expiration (no matter where the stock is trading), I'll have a profit of $1500 (less commisions)

    So now we can create a table that shows Calls and Puts

    Stock = 9.70
    Strike Call Put
    10.0 2.00 1.70
    7.5 3.30 1.10
    5.0 5.10 0.50

    Yes, deep itm options cost more because the likelihood of them being itm at expiry is higher - they have a delta closer to 100. BTW, the delta is a rough approximation that the option will finish in the money 85 delta ~ 85% chance of being itm at expiry. So you're paying money up front for the higher probability. Whether you make money on the trade is another. Hope this helps.
  3. def

    def Sponsor

    the answer lies with probability and leveraged returns....
    If you sell something deep in the money with a premium you could turn around and buy the stock and lock in a profit. no one will offer this to you.

    Take an extreme example. You buy a deep in the money call on a $100 stock. The stock goes up 10 bucks. most likely your option will only go up 10 bucks and you get roughly a 10% return. However, an out of the money option bought for say 1/2 could now be worth say $5. The magnitude of the return is enourmous in relation to the deep in the money call. In essence you are paying for the right to achieve such a return.

    in terms of put/call parity it may make more sense.
    C-P=forward value of the stock

    got to admit i'm a horrible technical writer and I didn't answer all of your questions. this may make no sense to you. if not, let me know and I'll spend some more time on it tomorrow.
  4. def

    def Sponsor

    i'm such a slow writer, i got beat to the punch by the previous response. between the two posts you should have an idea.