# Price improvement Contango protocol provides a better pricing than the theoretical formulas presented in the [theoretical pricing](/exchange/protocol/theoretical-pricing.md) section. This price improvement comes from the capital efficiency of using the trader's margin. ## Definition We define the price improvement as: * $$pi\_L=(P\_{th,L} - P\_{O,L} )/P\_{O,L}$$ for a long position * $$pi\_S=(P\_{O,S} - P\_{th,S} )/P\_{th,S}$$ for a short position. Knowing the [theoretical pricing](/exchange/protocol/theoretical-pricing.md) and using the [pricing formulas with the collaterisation ratio](/exchange/protocol/protocol-pricing/position-opening.md) to open a position, we find the following expressions for the price improvement:

Side	Price improvement
Long	pi_L={CR*[{(1+r_{Q ,b })}^T -1]}
Short	pi_S=\dfrac{CR[{(1+r_{Q ,l })}^T-1]}{1-CR[{(1+r_{Q ,l })}^T -1]}

## 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. * The higher the [collateriation ratio](/exchange/resources/glossary.md#collateral-ratio) $$CR$$ , the better the price improvement. * The higher the time to expiry $$T$$, the better the price improvement. * For a long position, the higher the interest rate on the quote currency $$r\_{Q ,b }$$ the better is the price improvement: compared to the theoretical formula, the protocol borrows less money and hence owes less debt. * For a short position, the higher the interest rate on the quote currency $$r\_{Q ,l }$$ the better is the price improvement: compared to the theoretical formula, the protocol lends more money and hence makes an extra profit. * 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 Here are different CR scenarios to open a long and short position for $$1 : ETH$$, where the spot price is $$ETHDAI=10000$$, with the corresponding price improvements: ### Long

Collaterisation ratio (CR)	25%	50%	100%
Theoretical price	101.81	101.81	101.81
Pricing with collateral	101.19	100.58	99.39
Price improvement	0.61%	1.22%	2.43%

### Short

Collaterisation ratio (CR)	25%	50%	100%
Theoretical price	101.51	101.51	101.51
Pricing with collateral	102.12	102.73	103.99
Price improvement	0.60%	1.21%	2.45%

## Simulations Here are some simulations to visualise the price improvement on long positions depending on the borrowing rate $$r\_{Q,b}$$. Similar results can be found for price improvements on short positions. ![](/files/hUE7MveQQskOegtdSShL) --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://contango-2.gitbook.io/exchange/protocol/protocol-pricing/price-improvement.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.