I’m wondering if you could help me determine if my logic/maths is correct!? I was looking at Currency Option payout probabilities:
The maximum premium received by Selling/Shorting/Writing Puts or Calls:
eg: Receive $187 premium (on a £/$ 1.2200 Put — Sept 18th expiry). This is a bullish strategy.
The probabilities if an option remains Out the Money (OTM) and worthless to the buyer, can be approximated from the Delta values from IG’s PRT Option Chain. Go to PRT: Display/Option chain. If there is a 90% (Delta) chance the option will expire worthless in September you get to buy the contract back for pennies and close it.
Surely the question should be what is the risk/reward probability outcome?
So I’ve created an Excel Table for all the Option probability outcomes – pls see attachment. The tables stop at 50:50 odds. I would only consider selling options with a high probability that they will remain OTM i.e. that the Delta is 20% or below. (The Delta is a percentage approximation for the option remaining In the Money).
Along the top rows are the payouts (which could be in €’s, £’s or $’s) by Shorting/Writing options (i.e. Open to Sell a Call or a Put). Down the first two left columns are the probabilities of the option expiring OTM. OTM is a good thing because as an option seller you can close the short contract by buying it back either for a few cents or for zero and it’s automatically closed.
So for example if the payout on an option is $185 in premiums, the table shows that with a 90% chance of being valueless to the purchaser at expiration, the maximum risk to take is no more than $1,665.
Reward = 90% x $185 = $166.50
Risk = 10% x $185 = $ 18.50
Reward Risk Ratio = 166.50 / 18.50 = 9
Therefore do not risk more than $185 x 9 = $1,665
Delta of 90% / 10% = 9
Is this correct math/probability?
So if you kept taking the same trade and receiving the same $185 premiums, trade after trade after trade, the odds are that over the long term you will come out ahead by keeping to this level of risk. Does that sound right?
Also what if you decided to only take perhaps 1/4 of this risk and close the losing option trade out at $400 instead of $1,665 does this increase your long term profitability or in fact not allow the odds to “play out” and instead result in you closing out trades too early without letting the odds play out and the underlying move against you?
I hope this makes sense,
Cheers
Bard