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# Chapter 5 Margin requirements for short Options

#### NEichi

##### New Member
Hi all,

I am a little bit confused about the margin requirements for short Options in Chapter 5 of the GARP book (i am working with the 2020 version). I am not sure if there is a mistake or if i am just missing something. GARP states, that the requirement for a short call is calculated as the greater of:

a) 100% of value of option plus 20% of underlying stock price less amount ( if any) that the option is OTM
b) 100 % of value of option plus 10% of underlying stock price

for a short put the requirements are the same for a) but in b) the stock price is replaced by the strike price

The given example is: 100 call options on a stock are sold for USD 5 per Option when stock price is USD 47. When strike price is USD 50 the option is USD 3 out-of-the money.

the calculated margin is

max(5+0.2x47-3,5+0.1x50)=11.4 in the second part of the Max-Function the strike price is used but this would be the function for a short put not a short call (in case of short call it must be 5+ 0.1x47 (the stock price) as stated above).

Are the formulars correct an there is just an error in the example or are the margin requirements for short call and short put identical and the part b) formula for a short call is wrong? I could not find it in the study notes, maybe i just overlooked them.

Thanks in advance

Nina

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @NEichi The formula is correct per Hull (who is GARP's ultimate source here) ...
"[10.7] Writing Naked Options As mentioned, a trader who writes options is required to maintain funds in a margin account. Both the trader’s broker and the exchange want to be satisfied that the trader will not default if the option is exercised. The amount of margin required depends on the trader’s position. A naked option is an option that is not combined with an offsetting position in the underlying stock. The initial and maintenance margin required by the CBOE for a written naked call option is the greater of the following two calculations:
1. A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount, if any, by which the option is out of the money
2. A total of 100% of the option proceeds plus 10% of the underlying share price.
For a written naked put option, it is the greater of
1. A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount, if any, by which the option is out of the money
2. A total of 100% of the option proceeds plus 10% of the exercise price. The 20% in the preceding calculations is replaced by 15% for options on a broadly based stock index because a stock index is usually less volatile than the price of an individual stock." -- Hull, John C.. Options, Futures, and Other Derivatives (p. 221). Pearson Education. Kindle Edition.
... but, I agree with you, GARP's interim formula has a typo. For the naked written call, it should be as follows (although the result is the same):

max(5 + 0.2 * 47 - 3, 5 + 0.1 * 47) = 11.4.

Great catch
on your part! Thanks,

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