Hello,
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For a long calendar spread, why is a stable market beneficial?
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For a short calendar spread, why is a big move in the underlying market beneficial?
Thanks!
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This becomes a pure theta play; prices on long-term options decay more slowly than prices on short-term options.
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Time value is greatest ATM; it falls off ITM and OTM.
If you have access to a BSM option pricing model, or you can create one for yourself in Excel, I encourage you to model these situations and see for yourself how the values of the spreads change. You’ll remember it much better if you do it yourself.
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Thanks @S2000magician
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Indeed this is a theta play. I guess my confusion is - so what if the market is not stable? Is an unstable market bad because large moves in the price of the underlying may cause the options to become ITM or OTM? And if this happens, the longer-dated option may start to decay faster than the shorter-dated option?
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In a similar vein to (1) above, shouldn’t a stable market be good for a short calendar spread? If we have large moves in the price of the underlying, the ITM or OTM options might become ATM. In this case, the shorted-dated options that we are long would now decay more quickly than the longer-dated options that we are short.
I hope I am making sense!
To answer from a different viewpoint.
For the long calendar spread, suppose you have a short call with maturity \tau_1 and a long call with maturity \tau_2>\tau_1.
Look at what happens right when the short call expires.
The long calendar spread is worth most when it’s ATM.
At that moment in time, if the stock price is below the strike price, the short call is worthless, so the value of the long calendar spread is simply the value of the long call, and that increases as the stock price increases.
Again at that moment in time, once the stock price exceeds the strike price, the situation changes. The short call is now in the money and you have to pay S-X (S stock price, X strike price) to the holder, so the value of the long calendar spread is now the value of the long call +X-S, and that decreases as the stock price increases.
There’s a rough plot of the value of the long calendar spread versus the stock price at the maturity of the short call. (for X=1, \tau_2-\tau_1=1 (that’s the remaining life of the long call), r=0.05, \sigma=0.25.)
The long calendar spread is worth most when S=X, decreases very rapidly as the stock price decreases away from S=X, and decreases less rapidly as the stock price increases away from S=X
For the long calendar spread, you want the value to be as high as possible so you pick something close to S=X.
For the short calendar spread, you’re on the other side of the long calendar spread so you want to be away from S=X
Thanks @guest , this is very helpful.
I understand that when the stock price exceeds the strike price, the value of the long calendar spread is value of the long call + X - S. So from this perspective, I understand why the the holder of the long calendar spread does not want stock price to increase.
But if stock price is below strike price, and both options are OTM, then the value of the long calendar spread is just the time value of the longer-dated option. Why is this bad? Is it because OTM options have lower time value than ATM options?
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Remember, I was only talking about the exact time when the short option was about to expire.
Exactly.
In my plot, the left of the plot (S<1) is the OTM case.
If you move just from S=1 to S=0.88, the value of the calendar spread drops by 50% (again only for this exact time).
- When the price of the underlying changes, it’s no longer a matter of time decay. It’s that the time value is greatest for ATM options, so lower for ITM and OTM options. And the longer the maturity, the greater the time value difference.
- In a word: no. If you hold a long calendar spread with a single counterparty, they hold a short calendar spread. Whatever is good for you is bad for them, and vice-versa, so whatever is good for a long calendar spread is bad for a short calendar spread, and vice versa.
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