# Modeling inverse mirrored assets peg

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

“Pathway: a protocol for algorithmic token pricing”

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.

Inverse sythns model

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.

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tickers for synths can be like:

gtonETHs - mirrored ETH

gtonETHi - mirrored (sigmoid) inverse ETH

gton{XXX}i/s

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Interesting proposal Alex, but it’s difficult for me. I hope some part of the community understand this. Let’s discuss! Wdyt???

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