Position opening
The formulas below present the price at which a trader could open a long position at a price
or a short position at a price
with an initial margin
(other notations have been introduced in theoretical pricing).
Side | Price to open a position |
---|---|
Long | |
Short | |
Contango protocol provides a price improvement compared to the theoretical formulas presented in theoretical pricing:
- Since, the price to open a long position is at a lower price, i.e. more favourable to the trader.
- Since, the price to open a short position is at a higher price, i.e. more favourable to the trader.
Let's consider a contract on ETHDAI expiring in 3 months (
) and where the traders posts
as margin:
- Given one could borrow DAI at a yearly fixed rate of, lend ETH at a yearly fixed rateand buy ETH on the spot market atthen the price at which a trader could open a long a position is:
- Given one could borrow ETH at a yearly fixed rate of, lend DAI at a yearly fixed rate ofand sell ETH on the spot market atthen the price at which a trader could open a short position is:
Let's consider that a trader wants to buy 1 expirable (the numerical values are taken from the above example). In this demonstration, we will present the steps to replicate the cash flows of a expirable position. Let's figure out the price of the expirable, i.e. the DAI money needed, to get 1 ETH at expiry:
1. To receive 1 ETH at expiry, the trader needs to lend
, i.e.
2. To get that ETH, the trader first swaps
, i.e.
.
3. Since the trader has already some margin, she only needs to borrow
, i.e.
.
4. The debt
the trader owes at expiry (principal + interest) is:
, i.e.
.
5. Hence, the money needed to receive 1 ETH at expiry is the sum of the debt and the margin provided:
or
, i.e.
.
Let's consider a trader who wants to sell 1 expirable (the numerical values are taken from the example above). This means she would give 1 ETH at expiry, let's figure out the steps and how much money she would need to receive at expiry:
1. The trader will give 1 ETH at expiry to reimburse a debt. Hence the trader borrows
, i.e.
.
2. The trader swaps the ETH to get
, i.e.
.
3. The trader lends the DAI from the swap and her margin. At expiry the trader receives an amount
, i.e.
.
4. The amount of money the trader will receive at expiry, which is also the price of the expirable, is the difference between the amount L and the margin:
or
, i.e.
.
- the margin for a long position could be expressed as, e.g. if the price to open a long position isand if the trader wants a margin ratio of 50%, then the required margin is
- the margin for a short position could be expressed as, e.g. if the price to open a short position isand if the trader wants a margin ratio of 50%, then the required margin is
Replacing the margin
in the main pricing formula to open a position, we find new expressions depending on the collaterisation ratio
:
Side | Price to open a position |
---|---|
Long | |
Short | |
Let's consider a contract on ETHDAI expiring in 3 months (
) where the trader puts a
MR:
- Given one could borrow DAI at a yearly fixed rate of, lend ETH at a yearly fixed rateand buy ETH on the spot market atthen the price at which a trader could open a long a position is:
- Given one could borrow ETH at a yearly fixed rate of, lend DAI at a yearly fixed rate of, and sell ETH on the spot market atthen the price at which a trader could open a short position is:
Last modified 5mo ago