Higher ROE from selling calls than selling puts?

Discussion in 'Options' started by theTaoTrader, Mar 30, 2005.

  1. Say the stock is $100 and we are selling ATM puts and calls (European options). The call premium will be worth more than put premium by the amount equal to interest earned on strike price $100 prior to expiration at risk-free rate (put/call parity). This is based on pure arbitrage argument, no option pricing theory involved. i.e. buying one share of stock and a put is equivalent to buying a call and deposit cash of ($100 - interest).

    Intuitively I understand that since buying a call with cash deposit will earn an interest, a call must be worth more than a put. This is however from options buyer's point of view. For sellers who sell naked options, the margin requirement is the same for put and call. Does that mean selling calls gives you higher return on equity (assuming the put and call have equal chance to be ITM)? Or does this imply that the call is more likely to be in the money than the put at the expiration day? But why is that? (OK, Stock price goes up generally. But what about options on interest rate like TNX?) What am I missing?
  2. Anseld


    when you own the put and long the underlying, you pay interest. if you're doing the call, you collect. but whatever the interest is, it's often already calculated by the marketmakers, and it's reflected in the bid/offer. you won't notice it as much in the front months as in the leaps. and unless you're an mm holding decent size in long or short stock where you'd be sensitve to i, rho hardly matters. if you're just interested in knowing which option has better value for the same strike level, just calculate the synthetic. and make sure you account for dividends (if any).
  3. TauTrader,

    You may overlooked IV (implied volatility).

    IV is far more important in option pricing than interest rates. As you know, IV is different for CALLs and PUTs. It also changes dynamically. CALLs IV is usually lower than PUTs IV. I believe the reason is that commercial traders use long PUTs (insurance) and short CALLs (part of covered CALL) much more than short PUTs and long CALLs.

    My advice to you is to select a liquid stock or index and look how ATM option pricing and IV change in real-time. This will give you better sense for how this works in real-life.

    For example: I'm sure you'll find that bid/ask spreads and intraday volatility both impact the feasibility of your proposed option trading strategy much more than any interest or arbitrage considerations.
  4. Thanks to both of you guys.

    The volatility smile in which the IV of puts differs from IV of calls exists only when the put and call have different strikes and/or expiration days. In my original example where the underlying and put/call strike are both $100, the implied volatility of the put has to be the same as the call’s IV (European options, no-arbitrage).

    In real-life we don’t see the underlying staying right at a certain strike very often. The MNX (MINI-NASDAQ 100 INDEX) is around 149 today. Say it reaches 150. We should see the April 150 call and 150 put at $2.16 and $1.97 respectively (17 DTX, 16% volat., 2.75% risk-free rate). The call is almost 10% higher than put! The $0.19 difference is the interest over 17 days on the face value of $150. That’s why it’s so significant. To a naked options seller, the margin requirement is the same for put or call (about 20% of this face value, plus/minus OTM, premium etc). So why the return on equity by selling naked calls is 10% higher than selling naked puts?

    when we calculate synthetic market (call - put), we are more interested in creating conversions or reversals, are we?
  5. Anseld



    well, first of all, the call is priced higher than the put at the same strike level (given the same iv) because the call has a higher delta level. that's just how the model(s) is (are) structured. buying calls will net interest, and puts will cost interest, and it evens out.

    also, since it's european style options that you're using, the put will be priced even less than the american style because of the nature of the lower delta.

    but in reality, that theoretical price difference of 19cents is not really as significant if you take into the full account of the price of the underlying, which is 150. more expensive underlyings will obviosuly have more expensive options, so that 19cents is not really that much if you consider that.

    at 149.8, the price scenario changes, and the options should be priced relatively equal over there because both will have about 50 level deltas. but again, those 0.20 is not really that much of a change for an underlying with a 150 price level to begin with.

    so if you bring down the underlying to, say, $15, and use the same parameters, you will see that there isn't really that much of a difference... maybe only 2 pennies.

    and if you use the original NDX options, the results will be consistent, and the difference would be about 2 bucks, but it's all relative.

    hope that helps.
  6. The scan risk might be the same, but the liuidation value of the call will be more than the put. So total margin requirement will be more for the call than for the put. At least that's the case using risk based margining (SPAN), maybe different with rule based margining.
  7. MTE


    Ignoring everything else (margin requirements and etc.), the reason that the call is more expensive is because, theoreticallly, the stock can go up to infinity, while down only to zero. So your potential risk on a naked short call is much greater than on a put, hence the higher compensation for a call.
  8. Not sure I understand the question, but

    in a flat vol world, calls would be priced higher than puts because of positive interest rates.

    Calls increase in value with interest rates, puts decrease in value with interest rates.

    Of course in the real world, vol is not flat and put vols tend to be higher than call vols for most equidistance strikes from ATM. So puts might be priced higher.

    Also, of course, dividends lower the value of calls and raise the value of puts, so we need to correct for that.

    But yes, in a no dividend, flat vol, positive interest rate world calls should be worth more than puts.
  9. Higher delta, that makes sense. I forgot that. Thanks.
  10. Now I think about it, the call does have a higher margin requirement potentially, i.e. the 10% rule. For the put it's premium + 10% * strike, but for call it's premium + 10% * underlying. And this is consistent with MTE's comments that underlying has higher upward movement than downward movement.
    #10     Mar 31, 2005