# How it Works?

The synthetic asset prices will be stochastic Markov processes with the prices moving up or down every second, with the size of each movement being derived from random cryptographic hashes. 

Each synthetic asset can be customized by changing key variables such as volatility, drift or Bernoulli factors. 

The following is a simple example of a synthetic asset that has 50:50 odds of moving up or down every second, with the size of each movement being random, based on a normal distribution.

$$
P\_t = P\_{t-1} + N(u,\sigma^2)
$$

Synthetic assets will follow either Arithmetic Brownian Motion (ABM) or Geometric Brownian Motion (GBM).

Traders can then either long or short the price and cash out at anytime to profit from fluctuation in the price.

<figure><img src="/files/IWkiOBnKUKYG3y1ttw4U" alt=""><figcaption></figcaption></figure>

Traders can also leverage up their long or short positions up to a maximum position limit.

Traders will be automatically liquidated once their equity falls below the max position thresholds. Traders elect to set this liquidation feature to either adjust the position to less than or equal to the max limit (partial liquidation) or to completely exit the entire position (full liquidation) once triggered.&#x20;

**Max Position Size:**

$$
n = \frac{\varepsilon}{\triangle\_{\max}}
$$

$$
n = Position ;  Size ;| ;\varepsilon = Equity ; | ; \triangle\_{\max} = Maximum ; Price ; Change; per; Second
$$

**User Liquidation Thresholds:**

$$
\varepsilon \le \sum\_{i=1}^{k} |n\_i| \* \triangle\_{\max,i}
$$

$$
i = Synthetic ;  Market ;
$$

On average the market is expected to have a 50:50 long to short ratio, making it a zero-sum game between traders. However, when this ratio does not hold, the open Crypta Bankroll will then take on the risk and cover the excess longs or shorts. To ensure the bankroll and liquidity providers are not taking on excess risk there will be market specific and market aggregate position limits implemented.&#x20;

$$
E\_i = \left| \sum n\_{\text{Long},i} ;-; \sum n\_{\text{Short},i} \right|
$$

$$
E\_i = \text{Excess market skew for a given synthetic market}
$$

**Market Specific Limits:**

$$
E\_i *\triangle\_{\max,i} \le 0.015*CLP\_{NAV}
$$

This means that a trade can’t be opened if it would cause the liquidity pool's risk to exceed 1.5% of the pools Net Asset Value (NAV) for a particular market.

$$
E\_i *\triangle\_{\max,i} \le 0.025*CLP\_{NAV}
$$

This means that at any given second the liquidity pool won’t risk more than 2.5% of the NAV for a particular market. If the exposure exceeds 2.5% per market the engine will automatically close out positions, starting with the largest positions contributing the most exposure.

**Aggregate Market Limits:**

$$
\sum\_{i=1}^{k} E\_i *\triangle\_{\max,i} \le 0.025*CLP\_{NAV}
$$

This means that a trade can’t be opened if it would cause the liquidity pool's risk to exceed 2.5% of the pools Net Asset Value (NAV) for all markets combined.

$$
\sum\_{i=1}^{k} E\_i *\triangle\_{\max,i} \le 0.05*CLP\_{NAV}
$$

This means that at any given second the liquidity pool won’t risk more than 5.0% of the NAV for all markets combined. If the exposure exceeds 5% the engine will automatically close out positions, starting with the market with the most excess exposure and the largest positions contributing the most exposure.

**Fees:**

The bankroll liquidity pool will make its long-run profit by charging small transaction fees per trade, acting the same way as a broker / exchange.&#x20;

Crypta uses the following aggregate market fee structure which acts similar to a market maker-taker fee schedule. The fee schedule is built to encourage traders to open positions to bring the market to equilibrium and minimize bankroll exposure. &#x20;

<table><thead><tr><th width="366">Aggregate Market</th><th>Long Fee</th><th>Short Fee</th></tr></thead><tbody><tr><td><mark style="color:green;">>80% Excess Long</mark>   (90% Long : 10% Short)</td><td>0.70%</td><td>0.30%</td></tr><tr><td><mark style="color:green;">>60% Excess Long</mark>   (80% Long : 20% Short)</td><td>0.65%</td><td>0.35%</td></tr><tr><td><mark style="color:green;">>40% Excess Long</mark>   (70% Long : 30% Short)</td><td>0.60%</td><td>0.40%</td></tr><tr><td><mark style="color:green;">>20% Excess Long</mark>   (60% Long : 40% Short)</td><td>0.55%</td><td>0.45%</td></tr><tr><td>Equilibrium   (50% Long : 50% Short)</td><td>0.50%</td><td>0.50%</td></tr><tr><td><mark style="color:red;">>20% Excess Short</mark>   (40% Long : 60% Short)</td><td>0.45%</td><td>0.55%</td></tr><tr><td><mark style="color:red;">>40% Excess Short</mark> (30% Long : 70% Short)</td><td>0.40%</td><td>0.60%</td></tr><tr><td><mark style="color:red;">>60% Excess Short</mark> (20% Long : 80% Short)</td><td>0.35%</td><td>0.65%</td></tr><tr><td><mark style="color:red;">>80% Excess Short</mark>   (10% Long : 90% Short)</td><td>0.30%</td><td>0.70%</td></tr></tbody></table>


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