# Dynamic Pricing Model

Due to the paucity in historical data of smart contract exploits, traditional actuarial pricing cannot be efficiently applied to Nsure products. High transparency in the crypto world makes it possible to utilize the concept of free market pricing mechanism, where capital demand and supply directly and heavily drive the price. Therefore Nsure designed the Dynamic Pricing Model using a beta distribution's 95% percentile with shape parameter being capital demand and supply. Premium is further adjusted by a risk factor to reflect the security level of the project, and a cost loading for claim settlement fee and other internal cost.

### I. Formula

### II. Property

The model has the following properties, which is in line with the expected pricing of DeFi insurance:

When capital supply is high, i.e. more power is backed for a risk, the premium rate will be low

When demand is high, i.e. more policies is sold out, the premium rate will increase

More token is backed for a risk, i.e. more popular, less volatile of premium rate change is, and vise versa for a less popular risk, the premium rate will be sensitive for large demand change to avoid pricing error

### III. Considerations for model selection and parameter calibration

#### Beta distribution:

Beta distribution is selected because it fulfills the below requirements

demand and supply can be perfectly factored in as the 2 shape parameters, and matches all the desired properties

#### 95th percentile:

If the data is sufficient enough, premium should be determined by dividing the mean loss divided by loss ratio. Here 95th percentile acts as a proxy of mean loss so that a buffer is set for the uncertainly in loss tail (in case the tail is heavier than beta).

#### Risk factor:

It takes care of the riskiness embedded in each project. It is based on the rating we given for each project. In the pricing of traditional insurance, similar factoring exists called underwriting tier, which is applied to the base premium rate. Without the Risk Adjustment Factor, premiums of 2 projects would be identical if their capital demand and supply are the same, which is unsatisfactory since the difference of riskiness in the 2 De-Fi may not be equal. By multiplying the risk factor, we are basically evaluating the risk by capping the premium rate.

#### Scale factor:

Demand (policy limit) and supply (staked Nsure) is scaled down to maintain a reasonable sensitivity of beta function output (premium rate) to its input (demand and supply).

#### Avg claim cost %:

This is the average ratio of assessment cost for one claim to annual premium. Since each policy is given only one free chance for claim, short-term policy (duration less than 1 year) should charge more for the additional free claim chance comparing to proportional annual policy, where claim assessment fee for each claim is estimated by the annual premium multiplied by the avg claim cost %

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