intraday time decay?

[spindr0]

Quote from dmo:

Spin, I think what you're saying is that if IBM is at 100, then the 100 call will be more expensive than the 100 put due to cost of carry of the underlying. That's true, but it's due to "where the underlying is." That's because the pricing model uses the forward price of IBM as the underlying price, not the current price of IBM.

In other words, imagine there's a year remaining until expiration and interest rates are 10%. So the cost of carry of IBM for 1 year will be $10 (the calculation is slightly different but I'm simplifying here). The "forward price" of IBM then is 100+10=$110. As far as your pricing model is concerned, you're pricing a 100 put and a 100 call with IBM at 110. So of course the call is more expensive than the put.

Good explanation. I think that now, I understand what I was saying

Now let's turn to part II - the cost of carry of the option itself.

In the example I gave with the 180 call and put with IBM at 100, I was talking about discounting the 180 call by the cost of carry OF THE OPTION. This is completely separate and different from calculating the forward price of IBM based on the cost of carry of IBM itself.

In other words, imagine IBM is at 100, and the 180 calls are worth 1.00. If interest rates were zero, the 180 put would have to be worth 180+1=81 (intrinsic value plus time value).

But let's say interest rates are 1% and there's a year remaining in your option. If you buy that 180 put for 81, hold it for a year and IBM doesn't move, how much have you lost? Of course you lost a point in time value. But you also lost the money you DIDN'T make by keeping that $81 in T-bills all year, earning 1% - about .81. Altogether you'd have lost 1+.81=$1.81.

But your pricing model has a heart, and takes pity on you. It figures it would be unfair for you to lose the dollar in time value AND the .81 in lost T-bill interest. It would be doubly unfair because the person who sold you that option would EARN an extra .81 by taking the proceeds of selling that option and buying T-bills. So right at the start, in Solomon-like fashion it discounts the option by the cost of carry - the T-bill interest that you would lose and the seller would earn. It will subtract that .81, and spit out a fair value of 81 - .81 = 80.19. Make sense?

OK, I've had a nap and it all makes sense... I should probably stop here

Given that:

Stock + put - carry cost = call (assume no dividend)

If we're looking the 180 options with IBM at 100, would it be fair to say that if the call is worth zero since it's so far of the money, the discounting of the put comes from the carry cost?

Stock + (put - carry cost) = 0

IOW, the put goes for less than intrinsic and that's essentially what you said about the pricing model having a heart?

Or IOW2, if the forward price of IBM is being used and if the call premium is higher than the put premium then if the call premium is zero then the put premium must be less than zero (sort of a negative extrinsic) which means that the put might be 79.19 (as per your 81 cent carry cost example) despite being 80 pts ITM?

 

[dmo]

Quote from spindr0:

Good explanation. I think that now, I understand what I was saying

OK, I've had a nap and it all makes sense... I should probably stop here

Given that:

Stock + put - carry cost = call (assume no dividend)

If we're looking the 180 options with IBM at 100, would it be fair to say that if the call is worth zero since it's so far of the money, the discounting of the put comes from the carry cost?

Stock + (put - carry cost) = 0

IOW, the put goes for less than intrinsic and that's essentially what you said about the pricing model having a heart?

Or IOW2, if the forward price of IBM is being used and if the call premium is higher than the put premium then if the call premium is zero then the put premium must be less than zero (sort of a negative extrinsic) which means that the put might be 79.19 (as per your 81 cent carry cost example) despite being 80 pts ITM?

With American-style options, the option can't be worth less than intrinsic value. That's because if the cost of carry of the option becomes too great you can always just exercise the option and realize its intrinsic value. But with European-style options yes, the cost-of-carry discount can bring the option's fair value under its intrinsic value.

 

[trade4succes]

Quote from leorc:

how does theta work intraday?

i know that if theta of an option is X then after one day has past the option will lose X in value, but does this losing process gradually happening during the intrday or is it occur after the market close for the day?

thx a lot for ur input~

I am not sure I am correct, as I forgot what theta etc. means, but I guess your question about intraday time decay comes down to:
1) is interest calculated overnight or real time? > overnight as far as i know, therefore there shouldn´t be intraday time decay.
2) time decay as in volatility risk until time of expiration: I suppose for every second the option loses time and therefore risk, theoretically there should be intraday decay, albeit inmeasurably small probably in most practical cases.

 

[spindr0]

dmo,

Occasionally I gamma scalp a straddle. Given the discussion of carry cost and theta of puts versus calls, I wondered if it made any difference whether one just used calls or just puts?

For example, I took a straddle position late last month. For each straddle bot, I also bot 18 shares to start off delta neutral.

At that time, I could have bot 2 calls and shorted -118 shares or I could have bot 2 puts and bot 82 shares. These two positions would also have been delta neutral (not sure if it's relevant but adding these 2 would be the same as doing 2 straddles and 36 shares).

Given that carry costs make calls pricier than puts, is there an advantage to doing this with stock and puts versus those the other combinations that involve calls? And given that my broker pays bupkus on cash balances, wouldn't that tilt things further in the direction of lower cost puts?

 

[jones247]

For gamma scalping, is it better to enter a long straddle or a synthetic straddle?

Although the synthetic saves on the theta decay, as well as an adverse impact to implied volatility, it does give up the positive effect of delta & gamma because as the strike moves farther OTM, the delta & gamma reduction softens the adverse impact of the loosing leg. Also, if IV is increasing, that also helps the loosing leg.

One more thing... more leverage with a long straddle than a synthetic long straddle...

Any thoughts on which is better...

thanks,

Walt

 

[dmo]

Quote from spindr0:

dmo,

Occasionally I gamma scalp a straddle. Given the discussion of carry cost and theta of puts versus calls, I wondered if it made any difference whether one just used calls or just puts?

For example, I took a straddle position late last month. For each straddle bot, I also bot 18 shares to start off delta neutral.

At that time, I could have bot 2 calls and shorted -118 shares or I could have bot 2 puts and bot 82 shares. These two positions would also have been delta neutral (not sure if it's relevant but adding these 2 would be the same as doing 2 straddles and 36 shares).

Given that carry costs make calls pricier than puts, is there an advantage to doing this with stock and puts versus those the other combinations that involve calls? And given that my broker pays bupkus on cash balances, wouldn't that tilt things further in the direction of lower cost puts?

Spin, you seem stuck with this idea that carry cost makes calls more expensive than puts. It doesn't. It just changes the underlying price from the current price to the forward price.

In any case, it's a moot point. With T-bills currently yielding about zero, you can reasonably use a cost of carry of zero, which eliminates the whole problem entirely.

As for your other question - if we're talking about options on futures, then I can say absolutely, positively, in both a theoretical sense and a real, street-level, practical sense, no, it doesn't matter whether you're long straddles, puts, or calls. If we're talking about, say, the 1000 strike, you can be long 50 calls and no puts, 50 puts and no calls, 25 calls and 25 puts, or 5 calls and 45 puts. As long as your delta is the same there is really, truly, honest-to-god no difference.

Theoretically there is no difference with stock options either, but practically there may be additional considerations. You could run into a hard-to-short situation so if you buy calls you may find it difficult or expensive to sell stock against it. It's possible the short stock could be called away, leaving you with no hedge. There may be different margin implications.

So for gamma scalping with stock options, you're probably better off buying puts and buying stock against it. That way you can scalp gammas to your heart's content and never have to sell stock short.

 

[dmo]

Quote from jones247:



Although the synthetic saves on the theta decay, as well as an adverse impact to implied volatility, it does give up the positive effect of delta & gamma because as the strike moves farther OTM, the delta & gamma reduction softens the adverse impact of the loosing leg. Also, if IV is increasing, that also helps the loosing leg.

One more thing... more leverage with a long straddle than a synthetic long straddle...

Where on earth do people come up with such misconceptions?

There is a reason that a position consisting of a long put and a long underlying is called a "synthetic call." It is because a synthetic call has the same gamma, same delta, same vega and same theta as a natural call.

The same is true for synthetic puts, synthetic underlyings, and synthetic straddles.

 

[spindr0]

Quote from dmo:

Spin, you seem stuck with this idea that carry cost makes calls more expensive than puts. It doesn't. It just changes the underlying price from the current price to the forward price.

OK, I'm stuck on that idea and I have no clue how the forward price factors into what I think I'm seeing.

Let's try a hypothetical. Priced today (theoretical), a $50 stock has the following:

$4.16 = Nov 50c (delta = .545)
$4.04 = Nov 50p (delta = .455)

other than the natural straddle +/- stk, delta neutral could be:

buy 2 Nov 50c and short 109 shares
or
buy 2 Nov 50p and buy 91 shares

With the call position, the option component cost me 12 cts more per synthetic staddle. Now it may be obvious to you but I have no clue where I make that extra 12 cts per syn straddle so that the result is the same as the person who does the put side.

 

[donnap]

Quote from spindr0:

OK, I'm stuck on that idea and I have no clue how the forward price factors into what I think I'm seeing.

Let's try a hypothetical. Priced today (theoretical), a $50 stock has the following:

$4.16 = Nov 50c (delta = .545)
$4.04 = Nov 50p (delta = .455)

other than the natural straddle +/- stk, delta neutral could be:

buy 2 Nov 50c and short 109 shares
or
buy 2 Nov 50p and buy 91 shares

With the call position, the option component cost me 12 cts more per synthetic staddle. Now it may be obvious to you but I have no clue where I make that extra 12 cts per syn straddle so that the result is the same as the person who does the put side.

Hi Spin,

Of course, your example assumes much higher interest rates than today's rates.

The extra .12 comes from interest paid on short sale proceeds.

We both know that the ave. retail doesn't earn i on short proceeds and for now we pay - but the option pricing assumes that we are all MMs - lol.

 

[jones247]

Quote from dmo:

Where on earth do people come up with such misconceptions?

There is a reason that a position consisting of a long put and a long underlying is called a "synthetic call." It is because a synthetic call has the same gamma, same delta, same vega and same theta as a natural call.

The same is true for synthetic puts, synthetic underlyings, and synthetic straddles.

My aim was Not to compare a synthethic call with a natural call, as I recognize the greeks are the same.

What I was trying to do was compare an option leg with a stock position(obviously my attempt was poor). For example, is it better to have a long put & a long call or a long stock and a long put? Although having the long stock position instead of the long call would reduce the impact of theta & a drop in IV, on the flip side it looses the benefit of delta & gamma...

Am I wrong here??? Nonetheless, which is better, especially considering the leverage factor...

Walt