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Types of Derivatives: Linear and Non-Linear

There are two types of derivatives – linear and non-linear. Linear derivatives involve futures, forwards and swaps while non-linear covers most other derivatives.

Types of Derivatives

There are two types of derivatives: linear derivatives and non-linear derivatives. Linear derivatives involve futures, forwards and swaps while non-linear covers most other derivatives.

A linear derivative is one whose payoff is a linear function. For example, a futures contract has a linear payoff in that every one-tick movement translates directly into a specific dollar value per contract.

A non-linear derivative is one whose payoff changes with time and space.

Space in this case is the location of the strike with respect to the actual cash rate (or spot rate). An example of a non-linear type of derivative with a convex payoff profile at some point before the option’s maturity is a simple plain vanilla option. As the option becomes progressively more “in-the-money,” the rate at which the position makes money increases until it approaches the linear payoff of the future.

Similarly, as the option becomes progressively more “out-of-the-money,” the rate at which the position loses money decreases until that rate becomes zero.

Delta and Volatility

With non-linear types of derivatives it’s possible to capture gains from volatility by hedging a portion of the option’s value.
This is called the “delta,” and it’s derived from the mathematical formula used to determine price as well from rebalancing the hedge as spot moves around and the delta changes.

For instance, we could buy a one-month $50 call option on ABC Inc., (see “What are Derivatives?”) which would give us the right to purchase 100 shares.

With the spot price at $50, the option is said to be “at-the-money.”

“At-the-money” options have a delta of 50%, so to “delta-hedge” the option, we would have sold short 50 shares.

If the ABC price proceeded to $25 the next week, we could buy back some of the 50 shares we were short (realizing a $25 profit on those shares).

Subsequently, any move back to $50 means we could sell more shares short again. If the ABC price went to $75 the next week, we could sell more shares short.

This would enable us to buy these shares back if the ABC price went lower before maturity. The more times we can delta-hedge the option (or “dynamically hedge” the option), the more profit we will realize.

Every time we realize a profit, we help to pay for the option. If you own an option and you delta hedge it, you’ll make money if the stock price goes up. You will also make money if the stock price goes down. You must, however, delta-hedge consistently in order to realize that profit.

At the end of the day, you will only make money if you have realized delta-hedging profits that are greater than the premium you paid away for the option.

Once you can understand delta hedging, then you can understand the way options are priced and what it means to determine good value in a premium.

If you buy an option, then you’re thinking that you’ll make more money dynamically hedging around it than you will pay in premium. If you sell an option, you think you’ll make more money in premium than you’ll lose in dynamically hedging the option.

Volatility

One of the prime determinants of the price of an option is the volatility, or the measure of how much the spot rate is expected to move around.

In a high volatility environment, the spot rate will be expected to move around aggressively and options premiums will be very high.

In a low volatility environment, the spot rate will be expected to move around very little and options premiums will be very low.

One of the key factors in making money in options is to understand the nature of volatility.

It has two important characteristics:

First, volatility isn’t constant; it changes over time. There might be specific events that will cause volatility to spike higher.

Second, volatility is statistically persistent; it trends. If it’s volatile today, then it should continue to be volatile. If it’s calm today, then it should continue to be calm.

Making money in options often means realizing that the trend in volatility has changed from calm to volatile (in which case you buy options at the beginning of the volatile period when options’ volatility are still low compared to what you expect actual volatility will turn out to be) or selling options when the trend changes from volatile to calm (and option volatilities are higher than what you expect them to be).

The lack of knowledge about these two factors is the biggest single stumbling block around the use of derivative products.
There are multiple other kinds of derivatives instruments important to a thorough understanding of derivatives markets. Those include swaps, contracts, and hedging practices.

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