Cost of Carry

Perhaps someone would clarify a query re the Cost of Carry calculation (and correct my calculation if necessary).

I need to determine the underlying at certain (last trade) times for options to determine implieds for various expiries.

Assume today is 1 August. Sep DAX future expires in 46 days, Dec in 137 days, etc.

The underlying for Aug and Sep DAX options is DAX Sep future at 46 days.

The underlying for Oct and Dec options is the Dec future. However, due to low volume/infrequent trades on Dec one cannot rely on it for a reasonable value at a given time. Therefore, I use the Sep DAX as a proxy and adjust via the Cost of Carry calc.

Example: 1 Aug, 11:37 am, Sep DAX = 5705.

Dec DAX = Sep DAX x EXP(RATE) x (DAYS/365)

= 5705 x EXP(3%) x (137/365) = 5763.

My first query concerns the ‘DAYS’ figure. Is it 137 (1 August to 15 December)?

The problem is, I’m extrapolating from an approximation of two futures’ fair values (of spot/cash), ie a future fair value from a future value. Is this correct or should I use the cash for the calc?

Finally, is this the correct calculation?

Any advice greatly appreciated. Thanks in anticipation.

Grant.

PS.

Someone asks re books lower down in the forum. If I may make a couple of suggestions: JC Hull, Options, Futures and other Derivative Securities (Prentice Hall); and DA Dubofsky, Options and Financial Futures, Valuation and Uses (McGraw Hill).

 

The difference between Sep and Dec futures contracts should be the cost of carry from Sep to Dec expiry.

In fact, the difference between Dec futures and spot DAX should be the cost of carry.

 

MTE,

So I should use cash as the underlying and 137 days (Dec expiry)?

Grant

 

I don't think it's the same thing. Using spot you calculate the cost of carry on index options not on futures options.

Actually, disregard my previous post, I'm not certain it is correct. I'll just leave it to more educated people than myself.

 

MTE,

I think you are correct re cost of carry.

The difference betwen index options and futures options is the former is cash settled if exercised, the latter is delivered or received if exercised prior to expiry.

Then again, this is (was) the difference between FTSE options, European-style and US-style. The latter had the greater trading volume.

However, I could never understand the rationale for paying a higher premium to buy the US-style; Euro- and US- are both cash settled on the same index so the early exercise option for which you pay a higher premium is pointless and therefore, effectively redundant. It no longer trades.

There are other features but I'm too tired to continue. Until next time.

Grant.