Who can help me with the following query on delta hedge

dontknow1987

Suppose Philips is worth €25 and a three month call option with a strike of €25 has a delta of 0.50. Assuming that a trader buys 1000 of these call options he will need to sell 500 shares to be delta hedged. If the next day Philips’ stock price goes to €27 the delta will increase to, let’s say, 0.70. This means that in order to be delta hedged the trader will sell an additional 200 shares at €27. The next day Philips’ stock price goes back down to €25 and the corresponding delta of the option goes back to 0.50, which means that the trader will buy back 200 shares at €25. Just from rebalancing the delta, the trader has made 2

infinitybenzo

I think you mean that the value of the option position would increase by *more* than 0.5*(27-25)*(qty of option), since delta is not constant. The value of the stock position would decrease by exactly (27-25)*(qty of option)/2.

SFoyil

thks for your reply and I get it now, because the value of option would increase about 50% of (€27-€25) in the unhedged position.

ohai Wrote:
-------------------------------------------------------
> Well, your call option has positive gamma, which
> means that if the underlier price increases, the
> delta of the option increases. You are long the
> option and short the stock. So, as the underlier
> price increases and you do not hedge, your long
> position increases (delta of option increases
> while qty is the same) and your short position in
> constant (delta of stock is constand and qty is
> constant). So, if the market moves one way and you
> do not hedge, you make money from the positive
> gamma. Does this answer your question?

Kapie

Well, your call option has positive gamma, which means that if the underlier price increases, the delta of the option increases. You are long the option and short the stock. So, as the underlier price increases and you do not hedge, your long position increases (delta of option increases while qty is the same) and your short position in constant (delta of stock is constand and qty is constant). So, if the market moves one way and you do not hedge, you make money from the positive gamma. Does this answer your question?