Looking at delta graph for a 2-yr to expiry, very deep ITM call (assume non-dividend underlyer) delta is very close to 1. Colleague's view is that this graph is incorrect and delta value should be: 1 * (2-yr Discount Factor) so assuming 5% interest per year, it should be (very roughly) 90% delta. My question is, who's correct (the graph or my colleague)? And can you give an intuitive explanation? Using the formula for N(d1) given in Hull I think the graph is right, but don't want to blindly follow an equation without some understanding.

If your option and underlying both exchange traded products then delta=1. If option is OTC, the delta=90%

the delta is one - if its deep in the money and does not pay a dividend it behaves just like a stock. you wouldn't exercise the option early even if it was American as it doesnt pay a dividend and you are not foregoing anything by holding the option rather than stock.

well, the delta of a forward is not equal to delta of a future, so we need to define what derivative we are talking about.

Quote well, the delta of a forward is not equal to delta of a future, so we need to define what derivative we are talking about.a call on a non-dividend paying stock

May be I was not clear. I see the difference in margined option vs OTC option as the same as margined forward (future) vs OTC forward. If margined forward has different delta than OTC forward, then this logic should apply for options, right?

QuoteOriginally posted by: PlainVanillaMay be I was not clear. I see the difference in margined option vs OTC option as the same as margined forward (future) vs OTC forward. If margined forward has different delta than OTC forward, then this logic should apply for options, right?no

Thanks for the replies, the argument for deep ITM call delta on non div underlyer being 1 makes sense. One counter-argument I thought of was that if the underlyer for a deep ITM call increased in value by 1 unit, the deep ITM call (at expiry) will be worth one unit more, so shouldn't that future-payoff be discounted by the DF (and therefore slope of payoff becomes scaled by the DF thus affecting delta)? Not sure how to counter this argument.

QuoteOriginally posted by: LearnerThanks for the replies, the argument for deep ITM call delta on non div underlyer being 1 makes sense. One counter-argument I thought of was that if the underlyer for a deep ITM call increased in value by 1 unit, the deep ITM call (at expiry) will be worth one unit more, so shouldn't that future-payoff be discounted by the DF (and therefore slope of payoff becomes scaled by the DF thus affecting delta)? Not sure how to counter this argument.how much is the deep in the money call worth ? if the strike is K then the premium is going to be ( S - K*df + small premium for the put). so if you sell for this premium then you have charged the buyer for the funding on the strike.