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So, when is it good to trade options using delta hedging? To understand this, we need to go back to volatility. As we explained in the second article in this series, the option price depends on the volatility parameter. Volatility tells how much the spot needs to move to equal out the time decay. If the option is priced using the correct market volatility and this volatility stays constant over the life of the option, the delta hedge will, on average, simply earn the risk free rate. This is the arbitrage argument used for deriving the Black-Scholes price and why to some extent Black-Scholes still works with discrete hedging. However, if the actual market volatility turns out to be greater than the current implied volatility of the option, then moves in the spot will, on average, result in a larger profit from the gamma than the bleed reduces the value of the option, thus returning an overall net profit. Vice versa, if the actual market volatility turns out to be below the current implied volatility, then moves in spot will, on average, be too small for gamma trading to compensate the bleed. In the latter case, selling the option and going long the signed delta hedge is a way to collect the excess time value component of the option premium.

In addition to the play on gamma, the strategy also becomes a play on the implied volatility. As we observed in the earlier article about pricing, the implied volatility changes over the life of the option. Usually, if the implied volatility is lower than what is subsequently experienced in the market, then the implied volatility will start to increase. Thus the long gamma strategy will gain additionally as the price of the option increases due to the increasing implied volatility. Likewise, if the implied volatility is high compared to the subsequent market moves, then the short gamma strategy will earn additionally on the fall in the option price from the decrease in implied volatility.

The reader of the first article in the series might notice that the profile of the long option and short delta strategy is very much like that of a delta-neutral strangle or straddle (which is just a strangle with the put and call legs having the same strike). However, there is an additional advantage. With the delta-neutral strangle, we depend on the spot to eventually move to one side; otherwise, the options expire worthless. With the long option and short delta combination, we can repeatedly re-balance the net delta position to obtain a profile that again makes money if the spot moves in either direction. This way, spot does not have to move anywhere over the lifetime of the option as long as it moves from day to day in either direction. So, with delta hedging, aka gamma scalping, you can now see that there is not a strict requirement to make a prediction about the direction of the market even when trading positions in single-legged calls or puts.

Steffen Gregersen

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