Convexity, or commonly known as gamma, is an important measure of a derivative’s value with respect to the underlying assets. Understanding the concept and its impact would greatly benefit traders on derivatives trading, as well as helping you preserve your assets from being forced-liquidated.

The Non-linearity of OKEX Perpetual Swap  

Let’s take OKEX Perpetual Swap as an example.

At OKEX perpetual swap trading, you can buy and sell contracts of a fixed USD value of Bitcoin (100 USD), and we call these inverse futures contracts. (Learn more about perpetual swap here: https://www.okex.com/hc/en-us/articles/360020149012-I-Introduction)

As the name suggests, these contracts have a non-linear nature because margin and PnL are settled with the underlying asset instead of the quote asset. Briefly, it means your loss in BTC on each contract does not correlate linearly with the movement of BTC/USD trading pair.

Let’s assume that you have 1 Bitcoin. The current price is $10,000. And one perpetual swap is worth $100 BTC/USD. Now, one contract costs $100/$10,000=0.01 BTC. If you buy 100 long contracts at $10,000, it costs you $10,000 (1 BTC).

Now, if the Bitcoin price goes up to 11,000 BTC/USD, one contract costs $100/$11,000=~0.0091 BTC, your gain is 0.01-0.0091=0.00091BTC for each contract. As you’ve longed 100 contracts, your total gain is 0.0009*100=0.9 BTC. For this $1000 move in trading pair BTC/USD, you gained 0.00091 per contract.

Then, if the price goes to $12,000 and one contract costs you $100/$12,000=~0.0083BTC, your gain will be 0.01-0.0083=0.0008 BTC per contract. Your 100 contracts will help you gain 0.83 BTC in total.

This $1,000 movement will only help you gain 0.0091-0.0083=0.0008 BTC per contract, which is less compared to the previous scenario.

If BTC price continues to go up to $13,000, $14,000, and $15,000, we can see that for every $1000 move, the PnL per contract will narrow from 0.0009 BTC to 0.0005 BTC.

Let’s do the same for opening short contracts, and the results are shown in the below figure. The long position line shows the PnL profile in BTC (%) with respect to the Bitcoin price in USD. The straight line is the PnL (%) return if the contract moved in a linear style, the curved line is the long perpetual swaps position’s PnL (%) return. We can see that you will lose more money when the market falls, and make less money as the market rises.

Therefore, OKEX perpetual swaps have non-linear PnL curve in terms of Bitcoins. Each succeeding move of the same extent in the price of BTC/USD does not produce the same amount of profit or loss denominated in BTC. 

Figure 1. Contract Size: $100 BTC/USD; Quantity: 100; Entry Price: $10,000

How convexity affects your trading?

Now, let’s add different leverage levels to the previous example.

The initial margin

= contract size * quantity / entry price / leverage

= $100 * 100 / $10,000 / leverage=1 / leverage

We add the leverage levels of 1x, 5x, 10x, and 20x on both short and long sides, and examine how large a price movement can cause bankruptcy, i.e. losing all your initial margin. We plot these bankruptcy points in vertical lines on both long and short sides. The result is shown in Figure 2.

As we can see, If you long 1 BTC at $10,000, with the leverages of 20x, 10x, 5x, and 1x, you will go bankrupt when the BTC price hits $9,524, $9,091, $8,333, and $5,000 respectively. If you short 1 BTC at $10,000 with 1x, because of the convexity, you will never get bankrupt. With the leverage of 20x, 10x, 5x, the bankruptcy points are $10,526, $11,111, $12,500.

Therefore, if you open short, you can use higher leverage than the long side, and you will get liquidated sooner if you long with higher leverage.

To conclude, going long will be liquidated faster if the market goes to the opposite direction. While going short will never get you liquidated because of convexity. This causes the margin requirements to increase in a non-linear style. This also explains why longs get liquidated quick in a bearish market.

Figure 2. Bankruptcy points

Conclusion

It makes sense that derivatives traders normally make their trading decisions based on the spot price. Indeed, spot price is a very important factor to the derivatives price. However, what is even more important is to have a deeper understanding of how the relationship between the two, in order to help you make a better decision

Reference

https://www.okex.com/hc/en-us/articles/360020149012-I-Introduction

https://futuresbit.com/understanding-non-linear-nature-of-inverse-futures/

https://blog.bitmex.com/category/crypto-trader-digest/?lang=en_us


Disclaimer: This material should not be taken as the basis for making investment decisions, nor be construed as a recommendation to engage in investment transactions. Trading digital assets involves significant risk and can result in the loss of your invested capital. You should ensure that you fully understand the risk involved and take into consideration your level of experience, investment objectives and seek independent financial advice if necessary.


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