Speculative Trading with Options: Volatility Plays

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In products with low leverage opportunities, like stocks, options are often sold for the ability to create extra leverage. For a product like FX where there is plenty of leverage to begin with in the retail segment that trades on margined accounts, it is interesting to see what options can additionally deliver. In this article we explain how options can be applied to make portfolio returns in dull markets as well as making money in volatile markets without predicting the direction of the spot.

In the prior article about pricing we said that the price depends a lot on hedging arguments. The hedging in the Black-Scholes model is done through trading the underlying. This hedging is referred to as delta hedging. The point is to replicate the payoff of the option by replicating the price moves in the option through spot. Looking at how the price of the option reacts to movements in spot, see Figures 1 and 2, we observe that call options appreciate when spot rises, whereas put options depreciate when spot rises. This is the foundation of the convention that delta is signed positive for call and negative for puts. However, the change in the option price is not the same for the same spot move across the curve. This is illustrated by drawing tangent lines to the price curve of the option. The slope of the tangent tells how much the price of the option moves with respect to the underlying in a localized area. The slope of the tangent is called the delta of the option and delta hedging in the Black-Scholes model works by holding the delta, thus replicating the option price, through the underlying spot in localized areas. Because the slope is different for different values of spot, hedging the change in option price requires dynamically re-hedging of the spot position as spot moves. The Black-Scholes model assumes that this can be done for all small moves in spot and that the option payoff thus can be perfectly replicated trading the spot. This is, however, not possible due to friction, but still works to some extent discretely as will be explained below. One particular thing to notice though is the curvature of the option price. The price always stays above the tangent. This implies that if we go long the option and short the signed delta in the spot, that would be subtracting the tangent at the current spot from the option price, see Figure 3, then whenever spot moves in either direction the portfolio will make a profit. This curvature in the option price with respect to the underlying is known as the gamma of the option. When going long an option and hedging away the delta we are said to be long gamma.

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It seems that this is the perfect strategy; we make money if spot moves, and spot is bound to move at sometime. We can then re-hedge to the new delta of the option and wait for spot to move again. However, there is the time value of the option to consider and as time goes by the value of the option decreases. The loss in time value is also known as the theta, decay, or bleed. Figure 3 illustrates the loss of time value.