# Price improvement

Contango protocol provides a better pricing than the theoretical formulas presented in the theoretical pricing section. This price improvement comes from the capital efficiency of using the trader's margin.

## Definition

We define the price improvement as:

Knowing the theoretical pricing and using the pricing formulas with the collaterisation ratio to open a position, we find the following expressions for the price improvement:

## Implications

Several interesting facts could be inferred from the above expressions:

The price improvement is always positive, i.e. the pricing of the protocol is more advantageous than the theoretical pricing for a trader opening long and short positions.

In the case of a long fully collaterised position (CR=100%), the price improvement is equal to the interest rate to borrow the quote currency. Making the assumption that the borrowing and lending rates are equal, the price improvement is equivalent to lend the margin at a fixed rate.

## Examples

### Long

### Short

## Simulations

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