The Gamma Problem for Straddles, Or Why VIX Futures Are Necessary
A straddle is a position comprised of one call and one put on the same underlying asset with the same strike prices and in the same expiration cycle. With E-mini S&P 500 December 2013 futures currently trading at 1748, a trader might buy the 1750 call and 1750 put expiring in December. Why? One reason traders buy and sell option straddles is to express views about the future volatility of the underlying. If you think a stock is likely to become more volatile and you believe that option implied volatility does not already reflect your expectations, then buying a straddle will give you exposure to volatility without any exposure to the direction of underlying asset prices. The familiar payoff graph for a long straddle is at fig. 1.
Fig. 1. Straddle payoff diagram. Source: TD Ameritrade
The white line shows the profit and loss on the day that a long straddle trade is initiated. The red and green lines show the same profit/loss curve one and two months later. One thing we notice immediately is that as the price of the underlying asset moves further away from the strike price of our straddle, the straddle behaves more and more like a simple long or short position in the underlying. To see why this happens, imagine that we buy calls and puts struck at 1750 and the futures then climb to 1900. The 1750 put we bought will have lost most of its value, so it will not have much of an impact on our position. At the same time, the 1750 call will be deeply in the money and will act more and more like the underlying. If our intent was to trade volatility expectations rather than price expectations, this is a big problem.
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