Derivatives

Why option price falls more than it rises for the same change in underlying

Venkatesh Bangaruswamy | Updated on January 09, 2021

Option price falls more than it rises for the same change in underlying

The maximum you can lose on a long call is the premium you pay when you buy the option whereas your gains can be higher. This is referred to as the asymmetric payoff. But if this payoff were the only truth, no trader would short options as that would be an unattractive game. So, there is a flip side to this payoff. First, options often expire worthless, which means you will lose your premium more frequently than you will generate profits from your long position. And second, option price will decline more than it will rise for the same change in the underlying price.

The Greek story

Suppose you are long on the 13,900 strike call when the underlying is at 14,000. The gains you will make on your long position if underlying moves up 100 points tomorrow will be lower than the losses you will suffer if the underlying declines 100 points.

To understand why this happens, we turn to option Greeks. Determining the value or the price of an option at expiry is simple-- in-the-money options have only intrinsic value and at-the-money options and out-of-the-money options are worthless. But what about the price of these options any time before expiry?

Using the Black-Scholes-Merton (BSM) model, we can understand how prices react to changes in the factors that drive an option. Because these changes are denoted by Greek letters, they are referred to as option Greeks. You can input spot price, strike price, time to maturity, risk-free rate and the option price into a BSM calculator and you will get the implied volatility and the option Greeks.

Delta, gamma and theta, three of the five Greeks, can explain why option price will decline more than it will rise for the same change in the underlying price. Think of delta as the speed of the option and the gamma as the turbo charger to accelerate the speed. So, greater the delta, greater the change in the option price with respect to a change in the underlying.

When you buy a call option and the underlying moves up, delta and gamma work in your favour because of which your long call position will gain in value. Theta (or time decay) will always work against your long position, which is the reason why your option cannot move one-to-one with the underlying. Worse yet, when the underlying declines, the delta will also work against your long position.

Now, the delta and the theta are of a larger magnitude compared to the gamma. So, when the underlying moves up, you have one large-magnitude factor (delta) working in your favour. But when the underlying declines, two large-magnitude factors (delta and theta) work against your position. This is the reason why long positions in options can be frustrating- your position can lose more than it can gain for a same change in the underlying price.

Optional reading

When the underlying moves up, the new delta (speed) is the old delta plus the gamma. When the underlying moves down, the new delta is the old delta minus the gamma. So, the gamma accelerates the speed of the option when the underlying moves up but reduces the option speed when the underlying declines.

Note that delta is the change in the option price for a one-point change in the underlying. So, if the underlying declines by one point and the delta (adjusted by the gamma) is 0.70, your option price will decline by 0.70. That is how the delta works against your long position when the underlying declines. Nevertheless, it is still a good indicator to understand how an option price can change when the underlying changes.

The writer offers training programmes for individuals to manage their personal investments. Looking to understand derivatives better?

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Published on January 09, 2021

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