Earlier this year we described pathway protocol as a way to maintain peg price for mirrored assets via AMM DEX liquidity interventions.

We mentioned that this approach can be used for mirrored/synthetic assets like Gold, Silver, Stocks, Crypto or Indexes. It’s easy for mirrored assets, but what approach we can use to model the peg of inverse assets?

**Problem:**

First approach: we can just use **inversePeg = 1/x**, where x - price of asset we re inverse mirroring. The issue here is that **if x → to 0, so inversePeg → Inf**. So, we can’t just use 1/x approach.

**Solution:**

Let’s use * Logistic function*:

This approach helps to fix the range of mirrored asset price within certain interval and push **inversePeg** to the asymptotical value when **1/x** is going to **Inf**.

**Example:**

Let’s take ETH price = 2764$

Let’s assume that min value for eth shouldn’t be below 138$ which is 5% of current value (95% drop).

So, we can model inverse mirrored asset as:

we re using some simple tricks to keep the scale of Synth and its inverse values.

**Conclusion:**

Within certain reasonable ranges this approach works to let traders an opportunity to short mirrored assets with its sigInverse assets.

For example:

asset price is dropping 4% sigInverse asset price is growing on 3.6%. So traders are able to hedge their position or take an advantage from taking of short position in it.

To let traders to trade with leverage we can use onchain/offchain lending protocol where **Synths** or **sigInverse** synths tokens can be borrowed or lended with different dynamic APR.

All such **Synths** or **sigInverse** synths tokens will be integrated into GTON Ex on GTON Chain shortly with GTON as *MoE (Medium of Exchange)* utility token.