Math

The Bonds, are price mechanisms that tries to sell tokens at a predetermined rate over a specified period of time. Assume a Seller wishes to sell one token in exchange for a another one. BondSale is launched by the seller, who configures five variables:

Variable	Description
bond_amount	The amount of tokens that the Seller wishes to sell. of token which Seller want to sale.
floor_price	Minimal (and starting) price of a selling token.
sale_time	BondSale exists at this time.
up_bound	Defines the percentage difference between ceil price and floor price.
velocity	Defines how quickly prices fall over time.

For each trade, we call the function

/src/math.rs

pub fn calculate_new_price(
    bond_sale: &mut BondSale,
    current_time: u64,
    buy_amount: TokenAmount,
) -> Decimal {
    let delta_time = current_time - bond_sale.last_trade;
    let sale_time = bond_sale.end_time - bond_sale.start_time;
    let time_ratio = Decimal::from_integer(delta_time.try_into().unwrap())
        / Decimal::from_integer(sale_time.try_into().unwrap());

    let delta_price = bond_sale.velocity * bond_sale.up_bound * bond_sale.floor_price * time_ratio;
    let supply_ratio = buy_amount.percent(bond_sale.bond_amount);

    let price = match { bond_sale.previous_price } < { bond_sale.floor_price + delta_price } {
        true => bond_sale.floor_price,
        false => bond_sale.previous_price - delta_price,
    };
    let jump = supply_ratio * bond_sale.up_bound * bond_sale.floor_price;

    bond_sale.previous_price = price + jump;
    bond_sale.remaining_amount = bond_sale.remaining_amount - buy_amount;
    bond_sale.last_trade = current_time;

    price + Decimal::from_decimal(50, 2) * jump
}

where current_time measures how much time has passed since the start of the bonds and buy_amount is how much trader wants to buy.

Locally, in trade_time, the price chart looks like this:

$$\frac{\partial \operatorname{token\_price}}{\partial \operatorname{time}} =-\operatorname{velocity\cdotp up\_bound\cdotp floor\_price\cdot \frac{1}{sale\_time}}$$