# Risk Premium

## What is Risk Premium?

When a trader requests an options trade, the OLP will open a position opposite the trader's requested options position, exposing itself to position risk.

Risk Premium penalizes trades that increase the OLP's Greeks risk and incentivizes trades that reduce risk, which is similar to TradFi's options market making strategy.

## Problems with Existing Models

Existing AMM-based options protocols typically hedge only Delta and Vega risks, which leads to poor capital efficiency and limitation for users to truly enjoy on-chain options trading.

**Limitations of Delta-Driven Risk Management**: A Delta-Neutral Strategy utilizing spot/futures can effectively respond to movements in the price of the underlying asset within a certain range, but it continuously incurs unnecessary hedging costs when the market is in a rectangle pattern. Furthermore, it is impossible to respond when the price moves more than a certain range (e.g. Gamma squeeze)**Inability to Hedge other Risk Factors**: Hedging Delta and Vega risk alone does not hedge the risk of non-linear Theta decay, which occurs as an options position approaches expiry, where Theta increases in magnitude affecting the decrease in option value. This also makes it difficult for traditional AMM-based models to support daily and 0DTE options

## Moby Factors in all Greeks

Moby, on the other hand, categorizes OLP's risk into Delta, Vega, and Theta, using its own SLE model and calculates the size of the risk generated by a trader's trade. The Greeks representing the risk of individual OLPs are calculated and monitored in real-time using the Black-76 model, just like options pricing model.

For details regarding how Moby derives Greeks, please read:

Deriving Greeks## Moby Factors in Risk Direction

Furthermore, Moby derives Risk Premium based on 'Risk Direction', which determines the risk direction of the trader's transactions.

Risk Premium functions similarly to the Bid / Ask spread in the options order book. In other words, Risk Premium is added to quoted Model Price based on the futures price and market IV to provide the "AMM-based Bid / Ask Price".

At this time, a larger Risk Premium is applied to trades that further increase the risk of OLP, which encourages traders to avoid trades that increase the risk of OLP and to trade in a direction that reduces the risk of OLP. In particular, if the change in the Greeks is in the direction of hedging the risk of the OLP, the Risk Premium will be charged as low as 1/10th, as an incentive to encourage trading.

## Moby Factors in Greeks Weight

Lastly, Moby factors in 'Greeks Weight,' which considers the impact of individual transactions on the overall Risk Premium.

The Greeks Weight for computing Risk Premium is derived by taking a random sample of trades based on the type of trade and inversely calculating the vector values that cause Risk Premium calculated from that sample to converge to the Target Spread.

By applying Risk Premium based on these Greeks Weights, it is possible to minimize the risk of OLP while providing a narrower spread than the main CEX in 50-80% of cases.

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