# Convexity

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## Definition of 'Convexity'

Convexity is a measure of the change in the value of an option in relation to the change in the underlying asset's price. It is a second-order derivative, and it is often used to describe the curvature of the option's price-to-strike ratio.

Convexity is a positive value for call options and a negative value for put options. This means that call options increase in value at a faster rate than the underlying asset's price, while put options decrease in value at a slower rate.

The convexity of an option can be calculated using the following formula:

```
Convexity = (?2C/?S2) - (?2P/?S2)
```

where:

* ?C is the change in the call option's price
* ?S is the change in the underlying asset's price
* ?2C is the second derivative of the call option's price with respect to the underlying asset's price
* ?2P is the second derivative of the put option's price with respect to the underlying asset's price

In general, options with higher convexity are more valuable than options with lower convexity. This is because options with higher convexity have a greater chance of experiencing large price changes, which can lead to larger profits.

However, it is important to note that convexity is not the only factor that determines the value of an option. Other factors, such as time to expiration, strike price, and volatility, can also play a significant role.

Convexity can be used to create a variety of option strategies. For example, a trader can buy a call option with high convexity and sell a call option with low convexity. This strategy is known as a straddle, and it can be used to profit from a large increase in the underlying asset's price.

Convexity can also be used to hedge against risk. For example, a trader can buy a put option with high convexity to protect against a decline in the underlying asset's price.

Overall, convexity is an important concept for option traders to understand. It can be used to make more informed decisions about when to buy and sell options, and it can also be used to create a variety of option strategies.

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