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Question on FX options & time-decay

  • #1
  • First Post: Oct 25, 2009 5:45am Oct 25, 2009 5:45am
Hello, I hope this is the appropriate forum to publish this in - it looks like it's the "mixed" forum, and I don't see any "Fx option" forum, so I'll try here:

I am reading up on the greeks, and I have a few doubts concerning time decay:

One is: why does timevalue of options decay more rapidly during the last month of the options life - this is typically the case, it seems. I don't understand the reason behind this acceleration, basically.

Another one is: does vega (say of an atm option) fall in a straight line towards expiry - or is there typically an acceleration somewhere in the lifetime of the option - like with timedecay?

Maybe the two are interconnected?

(I have seen some options-vids on youtube, but they all only confirm that time-decay accelerates towards the end of an options life - none of them explain why.)

A third one: I am not sure if the "typical" moment in the option's life when timedecay accelerates changes between assets (FX crosses) and assetclassest (eg. do stock options behave different to FX options in this regard - maybe stock options decay quickly from 40 days, and FXO's from 25 days - I really don't know)

These questions are probably not simple to answer, I imagine!
  • #2
  • Oct 25, 2009 6:19am Oct 25, 2009 6:19am
The closer to expiry an option gets, the less chance there is for the market to make a move in your favour; therefore, its value will begin to ‘decay’ (lose value). Options that are at the money (closest to the current market price) have the greatest rate of time decay.

More:

http://www.trading-plan.com/options_time_decay.html

hth...
The only way to get smarter is by playing a smarter opponent.
  • #3
  • Oct 25, 2009 1:31pm Oct 25, 2009 1:31pm
Thanks, that was a very useful link - a very well written piece, indeed!

However, my fundamental question "why" is not answered there, still.

I clearly understand that time-decay accelerates when there's around 30 days left. I just don't understand why. (There's probably a logical explanation to that, I'm sure.)
  • #4
  • Oct 26, 2009 8:43am Oct 26, 2009 8:43am
If you want to dig deeper than there are Black Scholes theorums and greek formulations to look for. I have a primer on them and another mathematical proof for time decay of options. These documents are not pretty they could help you only if you will be able to understand them.

Do google search for options. If you could not get anything let me know.
The only way to get smarter is by playing a smarter opponent.
  • #5
  • Oct 26, 2009 10:20am Oct 26, 2009 10:20am
Quoting claudiorosso
Hello, I hope this is the appropriate forum to publish this in - it looks like it's the "mixed" forum, and I don't see any "Fx option" forum, so I'll try here:

I am reading up on the greeks, and I have a few doubts concerning time decay:

One is: why does timevalue of options decay more rapidly during the last month of the options life - this is typically the case, it seems. I don't understand the reason behind this acceleration, basically.

Another one is: does vega (say of an atm option) fall in a straight line towards expiry - or is there...
Let's look at the very simple math of an option. I will work with the following assumptions:

1) You have bought 100K 1.4500 EURUSD strike call with 100 days until expiration for 100 pips. The EURUSD is trading at 1.4500 at the time making your call an At The Money (ATM) call.

When you go form 100 days to 99 days left you have lost 1% of the total days left for the call to expire. Assuming all things stay the same (price of the EURUSD, volatility, interest rates) the call should lose about 1% of it's value since it has less time to come into the money.

2) Now let's change the scenario a little bit. You have bought 100K 1.4500 EURUSD strike call with 10 days until expiration for 30 pips. The EURUSD is trading at 1.4500 at the time making your call an At The Money (ATM) call.

When you go from 10 days to 9 days left you have lost 10% of the total days left for the call to expire. Assuming all things stay the same (price of the EURUSD, volatility, interest rates) the call should lose about 10% of it's value since it has less time to come into the money.

So the way I think about the issue is that a day is a day is a day, but a day is relative to the time left on an option. 1 day out of 100 has a very different value to 1 day out of 10. The inflection point on the acceleration of the value of this day is around 32 days left on the option. Meaning 1 day out of 100 is about the same as 1 day out of 99 or 1 day out of 98.

But 1 day out of 30 is starting to get more important than 1 day out of 31 which was more important than 1 day out of 32, etc.

Hope that helps.
  • #6
  • Oct 26, 2009 2:14pm Oct 26, 2009 2:14pm
Thanks Scattergood, that was exactly the type of answer I was looking for - understandable. I am not able to understand the complicated maths behind the black scholes formula, but that doesn't preclude me from understanding options better, I think. So an answer like that is extremely helpful, thanks again!

Actually, I spoke to a colleague who knows a lot about options, and he explained that theta accelerates, and the acceleration is constant throughout the life of the option (if int. rates, market price, vol stay the same, of course).

The same phenomenon you have if you drop a tennisball from a very high altitude (or any altitude, really) - it will accelerate until it hits the ground, all the way, and at the same pace.

Does that make sense to you guys, and do you think it's a correct observation?

Thanks!
  • #7
  • Oct 26, 2009 3:21pm Oct 26, 2009 3:21pm
Not sure that the "ugly" docs (:-)) are what I need, so please only send them if it's no hassle...........
  • #8
  • Oct 26, 2009 3:29pm Oct 26, 2009 3:29pm
I have a contact to an instructor who teaches the theory behind a wide range of financial instruments, amongst them options.

Here's what he replied to this part of the question: changes between assets (FX crosses) and assetclassest (eg. do stock options behave different to FX options in this regard) - but this is probably not simple to answer, I imagine!

Theta is greater in magnitude when volatility is greater. For example if you assume that stocks are more volatile than exchange rates then the rate of time decay for a stock option is greater than the rate of time decay for a currency option and I think that the stock option's rate of time decay will increase more, earlier than the currency option's rate of time decay does. You need to be very careful in your thinking here. Theta is the effect of a change in time on the value of the option. Discussing the change in theta over the life of the option means the effect of a change in time on the effect of a change in time on the value of the option. So now we are talking about what is the effect of a change of volatility on the effect of a change in time on the effect of a change in time on the value of the option!!

In particular, I would enjoy receiving comments on the bit in red. Does that sound right to you? I would tend to agree. If vols are high, it's sort of "dropping from a higher point", so there's "more to loose", so to speak - and if time value has to reach zero - then probably theta accelerates earlier - but not 100% that my thinking is correct on this.

(The bit in green is an answer to a question I don't think I made.)
  • #9
  • Oct 26, 2009 6:33pm Oct 26, 2009 6:33pm
Quoting claudiorosso
I have a contact to an instructor who teaches the theory behind a wide range of financial instruments, amongst them options.

Here's what he replied to this part of the question: changes between assets (FX crosses) and assetclassest (eg. do stock options behave different to FX options in this regard) - but this is probably not simple to answer, I imagine!

Theta is greater in magnitude when volatility is greater. [i][color=red]For example if you assume that stocks are more volatile than exchange rates then the rate of time decay for a...
You have to be clear on what theta you are discussing, relative or absolute value.

To be sure, with a high volatility, an options initial value will be higher than one one with a low volatility. Here is how I think of it for a $20 stock:

A $1 option with 100 days will lose about $0.01 in the first day.
A $2 option with 100 days will lose about $0.02 in the first day.

The higher volatility is reflected in the higher initial value of the second option. So yes, the higher volatility option loses more in the first day, but not on a relative basis.

The RATE of theta is pretty constant in relation to time, and its formula is independent of volatility:

http://www.maxi-pedia.com/web_files/...definition.png

What this says is that Theta = - (Change in Option Value / Change in Time). Volatility isn't really involved, except tangentially in determining what the option value is in the first place.

On the other hand, vega or the rate of change an option price relative to the change in volatility of the underlying is:

http://www.maxi-pedia.com/web_files/...ption_vega.png

What this says is that Vega = (Change in Option Value / Change in Standard Deviation of the Underlying Asset). Again, time isn't really an issue except to the extent that the time to expiry effects the option's price to begin with.

Think of the value of an option like a wagon being pulled by 3 big horses all independently:

One horse is Theta, moving the price lower as each day passes.

One horse is Vega, moving price higher as volatility increases, and moving the price lower as volatility decreases.

The last horse is Delta, moving the price higher as the underlying's price approaches and exceeds the strike, and moving the price lower as the price moves away from the strike.

On any given day you have a combo of the three.
  • #10
  • Oct 27, 2009 2:53pm Oct 27, 2009 2:53pm
OK, scattergood - what's the deal? Are you a professional options-instructor

Honestly, it's rear that you receive such quality answers on a forum, you're very clear.

Thank you very, very much
  • #11
  • Oct 28, 2009 4:03am Oct 28, 2009 4:03am
Quoting claudiorosso
Not sure that the "ugly" docs (:-)) are what I need, so please only send them if it's no hassle...........
ok here is it......see the 2nd point, dependance of option price on time.
Attached File(s)
File Type: pdf sj145.pdf   113 KB | 658 downloads
The only way to get smarter is by playing a smarter opponent.
  • #12
  • Oct 28, 2009 11:05am Oct 28, 2009 11:05am
Quoting claudiorosso
OK, scattergood - what's the deal? Are you a professional options-instructor

Honestly, it's rear that you receive such quality answers on a forum, you're very clear.

Thank you very, very much
You are welcome. I have been trading for about 4 years and moved into options about 2 years ago. I took a lot of time studying options before I started trading them. I have been systematic in trading index options this year and been positive for the year with very little draw down.

I moved into forex options two months ago because the margin is so much better. 100 to 1 or more! The spreads are high, but worth it for the extra position size you can take on.

I am happy to say I am up nearly 30% in two months on forex option trading.

As I have gotten so much from this site, I figured I should give back in the way that I can.
  • #13
  • Oct 29, 2009 8:40am Oct 29, 2009 8:40am
I also transfered from Spot to Option recently.
I am studying the Short Stangels now, and I am thinking there got to be some Option Calculators out there for us.

An Option Calculator can calculate from the day opened, if I just input the strike price at day x, then I should be able to get out my Short Options worth after 1 of the two is excercised and price keeps going beyond.

Does anyone here know where I can find this kind of Option Calculator?

Thanks ahead.
Simple is powerful all the time.
  • #14
  • Oct 29, 2009 2:11pm Oct 29, 2009 2:11pm
Quoting RiverTrader
I also transfered from Spot to Option recently.
I am studying the Short Stangels now, and I am thinking there got to be some Option Calculators out there for us.

An Option Calculator can calculate from the day opened, if I just input the strike price at day x, then I should be able to get out my Short Options worth after 1 of the two is excercised and price keeps going beyond.

Does anyone here know where I can find this kind of Option Calculator?

Thanks ahead.
This is very interestig, shorting options, I mean. How do you choose the strikes? Do you place them at or a bit "beyond" support & resistence levels? This is the method I am familiar with.

I have also heard people say that you shuold look at the relation between the vega and the theta, or something - and not look at levels at all, but simple go for the options where you have the highest time decay, and where vega disintegrates the fastest. OR SOMETHING. (This second point is clearly not something I have anything like a good understanding of, as it will probably come across. I have just heard someone say that some sort of ratio between two of the greeks is the only thing that "professionals" look at when they short vol. They apparantly completely ignore levels in the market - could be interesting to understand this better.)
  • #15
  • Oct 29, 2009 2:14pm Oct 29, 2009 2:14pm
Quoting scattergood
I moved into forex options two months ago because the margin is so much better. 100 to 1 or more! The spreads are high, but worth it for the extra position size you can take on.
.
How much higher, approximately, would you deem that spreads are? And which provider do you use? Which options have the tightest spreads? Exchange traded options on indices, maybe?
  • #16
  • Oct 29, 2009 2:15pm Oct 29, 2009 2:15pm
Quoting NewFX
ok here is it......see the 2nd point, dependance of option price on time.
Thanks, NewFX - i opened the doc for 10 secs, and I already have shivers running down my spine :-) I will need to find some "quite time" before I look at it for real!
  • #17
  • Oct 29, 2009 9:39pm Oct 29, 2009 9:39pm
Quoting RiverTrader
I also transfered from Spot to Option recently.
I am studying the Short Stangels now, and I am thinking there got to be some Option Calculators out there for us.

An Option Calculator can calculate from the day opened, if I just input the strike price at day x, then I should be able to get out my Short Options worth after 1 of the two is excercised and price keeps going beyond.

Does anyone here know where I can find this kind of Option Calculator?

Thanks ahead.
RiverTrader, I have been trading Short Strangles on the equity indexes starting in February. I am happy to report that I am up about 18% so far, with only two months in the red, each one less than 2%. I moved this strategy over to Forex and have been selling strangles for about 2.5 months. Here I am up about 28% in those two months. The difference being mainly the extra leverage.

What you are asking doesn't quite make sense. A short strangle shouldn't have any of the legs exercised. You want to keep the premium and have everything expire worthless. If you want to be long or short the currency, then I am not sure that a strangle is what I'd look at.

As for the calculations, you just need a simple spreadsheet with a black scholes formula in it. I think PowerXL has a Black Scholes add in.
  • #18
  • Oct 29, 2009 9:56pm Oct 29, 2009 9:56pm
Quoting claudiorosso
This is very interestig, shorting options, I mean. How do you choose the strikes? Do you place them at or a bit "beyond" support & resistence levels? This is the method I am familiar with.

I have also heard people say that you shuold look at the relation between the vega and the theta, or something - and not look at levels at all, but simple go for the options where you have the highest time decay, and where vega disintegrates the fastest. OR SOMETHING. (This second point is clearly not something I have anything like a good understanding of,...
When you sell any option, or pairs of options like in a strangle, your main engine of profit is time decay, or theta. Your secondary engine is a lowering of volatility, which is reflected in vega. Price movement, or delta can be neutral or harmful to your position. I'll explain:

Lets assume the following:

1) The EURUSD is at 1.4500.
2) The volatility of the EURUSD at the time is 20%. What this means is that in 1 year there is a 68% chance that the EURUSD will be priced within 80% of 1.4500 and 120% of 1.4500. Basically that it +/- 20% is 1 standard deviation of price movement.
3) You sell a 30 day Call at 1.5000 and a 30 day put at 1.4000 for 25 pips each leg, or 50 pips total.

The most you can make on the trade is 50 pips, the amount of premium you collected. You have collected 500 USD on a 1 lot (50 pips x 10 USD per pip) and that is added to your account. The net open gain or loss is the 50 pips - the cost of buying it back.

At expiration, if th EURUSD is between 1.500 and 1.400 you keep all 50 pips, because you don't have to buy them back.

So now there are three things that can affect the cost to buy back the two options:

1) The distance of the EURUSD to each strike. In this case you start out not really caring, as a 100 pip move up causes the price to buy back the Call to go up, but the cost to buy back the Put goes down abou the same. However the next 100 pip move affects the Call more than the Put. This is the effect of net delta on your position.

2) The volatilty of the EURUSD. If the EURUSD starts to wildly move up and down, thus increasing volatilty, the cost to buy the options back may go up even if the price remains the same. This is because going forward, because of the higher volality in price movement makes it more likely that the EURUSD may move beyond the striks. If however the EURUSD starts trading in a narrower and narrower range, then the volatility drops, and the options become cheaper to buy back because the expectaiton is that the price won't move so wildly to one of the strikes.

3) Time decay, or theta. Each day that passes reduces the amount of time that the EURUSD has to move towards one of the strikes. In 30 days it is much more likely that the EURUSD could move 500 pips, than in 20, which is more than in 10.

It is the balancing of Delta (distance to strike), Vega (underlying's volatility) and Theata (time decay) that makes a short strangle successful.

I tend to choose 30-45 day strangles as I want to get into increasing theta as quickly as possible. I also tend to look for currency's who have already had an increase in volatility over the last 30-60 days as a) it means I can sell the options for more premium and b) volatilty tends to go down eventually and it doesn't expand forever. Last I look for a currency that is making a retracement from a significant move. Such retracements tend to go in up down up or down up down patterns which will limit the net distance a currency will move.

If you want I can post some charts of some of the trades I have done to explain my thinking.
  • #19
  • Oct 29, 2009 10:09pm Oct 29, 2009 10:09pm
Quoting claudiorosso
How much higher, approximately, would you deem that spreads are? And which provider do you use? Which options have the tightest spreads? Exchange traded options on indices, maybe?
Spreads on options on index ETFs == $0.01 to $0.05
Spreads on options on forex ETFs == $0.01 to $0.05
Margin for ETFs == Lots x 100 x Strike x .2 - (Lots x 100 x (Strike - Underlying)

Lets say you sell the 1 lot of the SPY (S&P 500 ETF) Call at 100, with the underlying at 95.

Margin at time of purchase = 1x100x100x.2 -(1x100x(100-95)) = 2000 -500 = 1500.
Margin if SPY is at 100 = 2000 - 0 = 2000 or 20%

For a strangle you only need to have margin for one side, the closer strike so you can get the margin down to 10%.

===============
Spreads for options on Forex == 10 - 20 pips (I use a broker that fixes the spread to 10 pips for nearly everything I trade).

Margin for options of Forex == Lots x 100,000 x .02 x Delta (The delta of an At the Money (ATM) option is .5)

Lets say you sell the 1.5000 call on the EURUSD when the udnerlying is at 1.4500 which would make your delta around .15 - .2

Margin at time of purchase = 1x100,000 x .02 x .15 == $300
Margin if EURUSD is at 1.5000 = 1x100,000 x .02 x.5 = $1000 or 1%

For a strangle you only have to have margin on one side, so you can get the margin down to .5% or lower at times.

So the higher spread means I pay a lot more to exit trades, but the exta size I can trade is worth it. Hope that helped.
  • #20
  • Oct 30, 2009 12:18pm Oct 30, 2009 12:18pm
scattergood,

I will need to read your posting over and over to understand it all.
My worst nightmare is that Short Strangles are unlimited lost if strike price going outiside of this strangle set.

So, I am looking for a way to calculate out when is my maximum lost = 0, then I will simply close them all out, before expiration.

Can you show us how to calculate out the pips we can tolerate for maximum lost = 0, while the strike passes each option? (before expiration)

RiverTrader
Simple is powerful all the time.
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