# New Solution: Bonding Curve Mechanism

For more stability on-chain and a lower liquidation risk at loans, we introduce a new bonding curve mechanism which uses decentralzed dynamic insurance to rebalance the price from huge sell-offs from the boning curve mechanism and real live prices out of an oracle structure.

## Real Estate Value

The objective is to have an accurate, low-cost, and efficient mechanism for real estate price approval, while also accounting for the condition of the asset. We make use of an oracle structure combined with an insurance mechanism to manage price volatility.

**Oracle Structure**

**Oracle Structure**

Our oracle structure consists of:

**Entry Points**: These are data providers that submit raw data regarding real estate prices and conditions.**Validators**: Validators verify the accuracy of the data provided by the entry points.

**Independent Ratings**

**Independent Ratings**

Our system employs independent ratings, which differ from conventional ratings. Each rating undergoes an adjustment where we subtract a certain percentage, $x$ to ensure that we have a buffer against sudden price fluctuations.

**Insurance Mechanism**

**Insurance Mechanism**

From each rating, we extract a certain percentage and store it as insurance. This insurance pool serves as a buffer against significant price fluctuations.

#### Parameters:

Parameter/Variable | Description | Input/Output |
---|---|---|

| Original real estate value from the oracle | Input |

| Percentage deducted for insurance | Input |

| Adjusted Rating after deducting insurance | Output |

| Insurance Amount stored | Output |

**Price Fluctuation Buffer:**

To prevent significant loss in value from sudden price changes, the adjustment factor $x$ serves as a buffer.

**Oracle Validation:**

Ensure that the difference between the highest and lowest values provided by entry points does not exceed a predetermined threshold, $T$. If it does, further validation is necessary.

If ( D > T ), Initiate additional validation.

If ( VD > BA ), utilize ( IA ) to compensate.

### Bonding Curve for Pricing

A bonding curve is a mathematical curve that defines the price of a token based on its supply. In the context of NFTs for real estate, the curve can help set dynamic pricing based on demand, providing both buyers and sellers with a transparent pricing mechanism.

#### 1. Base Price Calculation:

**Formula:**

$Pbase=f(V)$

Where:

$Pbase$ is the base price.

$V$ represents valuations or assessments.

$f$ is a function deriving the price from valuation data.

#### 2. Buffer Zone Determination:

Define a range $R$ as the buffer zone above and below the base price.

**Formula:**

$R = P_{\text{base}} \times \frac{\Delta}{100}$

Where:

$Δ$ is the percentage defining the range of the buffer zone.

Thus, the buffer zone limits are: $Pmin=Pbase−R$ ;$Pmax=Pbase+R$

#### 3. Bonding Curve Mechanism

**Formula:**

$P=Pbase+C×Sα$

Where:

$P$ is the price on the curve.

$C$ is a constant that determines the steepness of the curve.

$S$ is the token supply.

$α$ is an exponent typically between 1 and 2. The value of $α$ determines how aggressively the price changes with supply.

Note: The value of $P$ must always be within $Pmin$ and $Pmax$.

#### 4. Price Setting and Dynamics:

**Implementation Mechanism:**

**Initialization**: Set the price to $Pbase$.**On Purchase**: Increase the token supply and compute the new price using the bonding curve formula.**On Sale**: Decrease the token supply and recompute the price.

#### 5. Hard Boundary Checks:

Ensure price remains within buffer boundaries.

**Check:**

$Pmin≤P≤Pmax$

If $P=Pmax$, consider using auction-based systems or revaluation. If $P=Pmin$, other mechanisms like lower limit price protections could be invoked.

#### 6. External Data Integration via Oracles:

**Oracle Mechanism:**

**Data Fetch**: Integrate with trusted oracles to get updated valuations or assessments.**Update Mechanism**: If a new valuation $V′$ is significantly different from the old valuation $V$, update the base price $Pbase$.

**Formula for Updated Price:**

$Pbase′=f(V′)$ Where:

$Pbase′$ is the updated base price.

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