Delta Hedging

Guys, can you please check the following note I have for Delta Hedging? “If underlying asset’s price increases, the delta increases and therefore the manager must borrow at risk-free rate to increase the position in underlying to maintain the delta hedge position. If underlying asset’s price decreases, the delta decreases and therefore the manager must sell the position in underlying (and invest the proceeds at risk-free rate) to maintain the delta hedge position” Shouldn’t it be other way around, meaning that shouldn’t delta DECREASE as the underlying asset’s price increases? (Delta for Call Option = (C1-C0) / (S1-S0)). If S1 increases, shouldn’t the Delta decrease?

For call options, delta increases as the underlying price increases. You can see that if you picture the option payoff chart. Delta is simply the slope of the option’s value. As you move to the write, the slope (delta) steepens => delta increases…

ok, so are we saying that as the price of the underlying increases, the price of call option increases even more, resulting in increase in Delta?

Before I say it is true, let me clarify something. The option value does not increase by more than the price change in the underlying security. Delta of one option cannot exceed 1. In other words, if the stock price goes up by $1, and we are at the money, the value of the option will change by 50c. Tomorrow, the underlying price goes up by $1 again. The value of the option will now change by 53c. And so on and so forth… So it is true to say that as the price goes further in the money, the option value changes at a faster rate than if we were out of the money.

thanks, kurmanal. I get it now.