parity and arbitrage

Discussion in 'Options' started by RainmanRam, Jun 4, 2009.

  1. I'm new to options and have some outstanding in the money covered calls coming due this month. I'm considering rolling the up and forward for a credit but have a timing question.

    Looking at the positions, they are currently 2% of the underlying from parity. At what point do I start risking arbitrage assignment? Are there any metrics that would help time this decision? I'd imagine volitility would have to be taken into account somehow.

    One position is on a $10 underlying and the other is on a $27 underlying. So the minimum bid/ask spreads come in at .5% and .2% respectively. I'd suspect the .5% would be more at risk of arbitrage but have no idea how to relate the two.

    Any insights or suggestions would be welcome.

  2. I'd love to help, but I find the lack of details so overwhelming that I simply do not understand what you are asking.

    What does 'they are 2% of the underlying from parity' mean? You say the options are ITM.

    Is it 2% in the money?

    Is the premium over parity 2%?

    What the heck is 'arbitrage assignment?'

    How about this:

    Ask again. Omit commentary and just provide details.
    Stock price, option strike. Bid/ask if you care to supply it. What option do you want to roll into. etc


  3. CLF trading around 28.31
    Short the Jun 24 call bid 4.60 ask 4.80
    Thinking of rolling to the Jul 25 call bid 4.90 ask 5.10

    I've seen the net credit higher than this but that's not relevant.

    The Jun 24 with a bid of 4.60 is .29 from parity which is just over 1% the underlying.

    As the option gets closer to parity the chance of assignment by arbitrageurs increases significantly.

  4. 1) You are mistaken. The chances of being assigned prior to expiration remain near zero. Unless there is a dividend between now and expiration, there is no possibility that anyone with a working brain will exercise a call option sooner than necessary. And arbitrageurs have working brains.

    2) If you are assigned, what's so bad? You earn the maximum profit that this investment can make.

    3) If you want to roll, forget how much premium remains in the option you want to buy. For example, if the July call were trading $3 higher and the June call, $1 higher, would you refuse to buy the June call - just because the premium was 'too high'? Would you ignore the fact that you can collect $2 more for the spread?

    You want to roll. How much do you want to collect for that roll? Once you know how much, then roll when you can get it and ignore the prices of the individual options.

    Note that rolling continues your risk to the downside, and allowing yourself to be assigned locks in the profit. Which do you want to do? Is the profit potential sufficient to carry the risk?

    Do you want to own the Jul Covered call at these prices? If yes, roll. If 'no' wait for better prices.

    Those are things that should matter to you - not the premium remaining in the call you want to cover.

    4) If you sell the stock via assignment, so be it. Find another stock to trade. You are not married to this one.

  5. 1) I don't think I'm mistaken. If I am than so is McMillan who also states "if the option begins to trade at parity or a discount, there arises a significant probability of exercise by arbitrageurs" ("Options as a Strategic Investment" page 83). I'd assume he means that if the option starts trading at a discount the arbitrageurs would step in and start assigning to pickup the discount.

    2) Nothing. However, rolling forward has to considered as a possibility for the best use of the money going forward. Assignment might also have tax implications (wash sales).

    3) Partially agree.

    Your right that I should just determine what I'm willing to take for gains and enter the spread order to obtain that gain. Being new to this, I don't want to leave excess money on the table (call me greedy). Since the near term option will approach parity faster than the far term one, I thought there might be a way to determine what the optimal spread might be.

    You are also right that rolling forward continues my exposure to risk but at the same time it also lowers the breakeven point by the credit received. I might not be able to obtain that breakeven point elsewhere so it should be taken into consideration.

    4) Yes. I agree. However, it is often easier to keep up with a single company you are already familiar with than it is to research a new company and its options (call me lazy). Perhaps even switching to a bearish stance.

    Thanks Mark. Your comments helped me to clarify my thoughts. I'll attempt to define my exact criteria for the roll and enter a spread order that meets that criteria.

    - Ray
  6. Note:

    Its not that McMillan is wrong its just that there is no incentive for anyone to exercise the option early unless there is a dividend play. The option will NOT trade below parity.
  7. Mark
    The Rookies Guide to Options
  8. I'm enjoying the conversation as well. Thanks for taking the time Mark.

    I am definitely a rookie and have learned a lot over the last month just by watching my positions. This discussion is very thought provoking for me and it will not be dismissed without thought. Why ask a question if you don't want to hear the answer? I realize I have a lot to learn and that will keep me asking questions.

    You know what they say about free advise though...

    I'm kidding of course. I highly appreciate it.

    There is (and I have) a lot to learn about options and how to best take advantage of them. I've said before that this forum is a valuable resource and this discussion reinforces that.

    - Ray
  9. Wrong.

    "It can be proved under essentially the same weak assumptions that
    the above put-call parity relation does not hold for American-style
    options. Here is a rough outline of the proof.

    Consider the case of a non-dividend paying
    stock and a strictly positive interest rate.
    Then, a similar arbitrage argument to the above shows that for a
    european-style call option with price c, it must be true that c > max[0, S - K e^(-r T)].
    Since an American-style call C is always worth at least as much, C >= c > S - K.
    But if C > S - K, then the option will never be exercised, so C = c.
    That is, an American call has the same value as a
    Euro-style call when there are no dividends and early exercise for it is
    never optimal.

    But, under the same circumstances, things are quite different for the put.
    An American-style put is worth strictly more than
    its Euro-style counter-part. To prove it, assume otherwise. Then,
    since a perpetual Euro-style put is easily shown to be worth zero,
    a perpetual American-style put must be worth zero.
    But this is a nonsense conclusion since an American style put must not decrease
    in value as the time to expiration increases. The premise must have
    been wrong, so under a no-dividend assumption, the American-style put value P is
    strictly greater the Euro-style value p. Hence P > p = C - S + K e^(-r T).
    In words, the American-style put value is *strictly larger* than the value given
    by the put-call parity relation. For more details see:
    R.C. Merton, "Theory of Rational Option Pricing",
    (Bell J. of Economics and Mgt. Science, 4, 1973, 141-183.)


    "The relation doesn't hold for American-style options, which
    allow an early exercise prior to expiration. For example, one
    of the options legs in the conversion trade may disappear
    prior to expiration because of an exercise/assignment. Closing
    the whole trade at this point produces a gain/loss that is
    unknown when the conversion is initiated.
    Not closing the trade leaves a risky position. "

    So, there is no call put parity for american style options.
  10. "Its not that McMillan is wrong its just that there is no incentive for anyone to exercise the option early unless there is a dividend play. The option will NOT trade below parity."

    Are you only talking about calls? I've had short puts exercised against me with months left on them.
    #10     Jun 9, 2009