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Gamma and dynamic replication - confusion
Posted: April 23rd, 2008, 10:26 am
by GM
Hi,I buy a call option and am long delta and long gamma.If I try to replicate the call by dynamically trading the stock, I buy delta units of the stock. I need to own more of the stock as the price goes up and less as it goes down. This is a "buy high, sell low" strategy as described in Hull. Therefore I pay a cost for rebalancing my delta. I am short gamma.If I try to replicate a short option (call or put), I gain rather than lose on my rebalancing strategy.What am I missing here??
Gamma and dynamic replication - confusion
Posted: April 23rd, 2008, 10:31 am
by Martinghoul
You're replicating the wrong way around, m8... Actually, you're replicating the right way around, which means that you're basically not rebalancing your delta, but rather doubling it up.
Gamma and dynamic replication - confusion
Posted: April 24th, 2008, 1:46 am
by midastouch
Yes, Im confused too. Let me see if i can get it right:When long option and gamma, and doing delta hedging (socalled scalping gamma), we gain on gamma because we want to make our option delta remain constant.On doing replication with stock, we long delta units of stock, and if we do maintain delta constant, then, we dont need to buy more as price goes up (and presume to be above ATM). If its below strike, then we have to liquidate the delta units below strike (sell below initial purchase), thus, we would be "paying" premium if it goes below strike.
Gamma and dynamic replication - confusion
Posted: April 24th, 2008, 12:00 pm
by sjcon
Why do you pay a cost for rebalancing your delta? You only buy more stock if it goes up, making all your old buys good buys and same with sells. Eg, stock is going up, you are buying more getting longer, you decide to 'hedge' your gamma so you are flat deltas again (say you sold 5k stock to do this), now stock starts going down so you start selling, returns to original level you are net short 5k stock, you decide to hedge' your gamma again. Net result is + cash.
Gamma and dynamic replication - confusion
Posted: April 24th, 2008, 12:00 pm
by sjcon
Why do you pay a cost for rebalancing your delta? You only buy more stock if it goes up, making all your old buys good buys and same with sells. Eg, stock is going up, you are buying more getting longer, you decide to 'hedge' your gamma so you are flat deltas again (say you sold 5k stock to do this), now stock starts going down so you start selling, returns to original level you are net short 5k stock, you decide to hedge' your gamma again. Net result is + cash.