> For the complete documentation index, see [llms.txt](https://seablocks-finance.gitbook.io/seablocks.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://seablocks-finance.gitbook.io/seablocks.finance/product-overview/usdi/underlying-derivatives/inverse-vs-linear-contracts.md).

# Inverse vs Linear Contracts

## **Understanding Inverse vs. Linear Contracts**

A **linear contract** follows a straightforward pricing model and is commonly used in many derivative markets. The price of a linear contract is expressed as the value of the underlying asset relative to the base currency. For example, a BTCUSDT perpetual contract is a linear contract, where BTC is quoted in USDT, and all margin and P\&L calculations are denominated in USDT.

An **inverse contract**, on the other hand, is denominated in a fixed amount of the quote currency. For instance, in a BTCUSD perpetual contract, each contract represents $1 worth of Bitcoin at any price level. BTCUSD is considered an inverse contract because it is quoted in BTC/USD, but the underlying value is derived from USD/BTC, effectively following the formula: 1 / (BTC/USD). This inverse structure allows traders to hedge USD values efficiently while aligning with the spot market convention of quoting asset prices in USD.

## **Convexity Implications**

Convexity (also referred to as Gamma) measures the second derivative of a contract's value relative to price changes. In inverse perpetual contracts, this relationship differs from the straightforward linear movement seen in linear contracts.

For a **linear contract**, the payoff is calculated as:

**Contract Multiplier × (Entry Price - Exit Price)**

For an **inverse contract**, the payoff follows a different formula:

**Contract Multiplier × (1 / Entry Price - 1 / Exit Price)**

This introduces convexity into the pricing model.

**Example:**

A trader enters a long position with 50,000 BTCUSD contracts at an entry price of $10,000 per BTC.

If the price rises to $11,000:

* Profit = 50,000 × 1 × (1/10,000 - 1/11,000) = 0.4545 BTC

If the price instead drops to $9,000:

* Loss = 50,000 × 1 × (1/10,000 - 1/9,000) = -0.5556 BTC

The greater loss in the downward move is due to the inverse, non-linear nature of the contract. Conversely, if the trader were short, the profit from a price drop would be larger than the loss from a price increase due to the same convexity effect.