The initial working draft of Convexity protocol was published in November 2019, paper found here. Zubin Koticha, founder and CEO of Opyn (dapp for insuring your DeFi deposits) has drafted the proposal as a mechanism/strategy for deposit insurance and risk hedging.  

Options writers can deposit crypto-collateral and mint options as ERC-20 tokens (oTokens, the new DeFi primitive of options contracts) as per their specified parameters (e.g. underlying asset, strike price, expiry date, etc.) in return. Writers can earn premiums by selling options to buyers as yet another way to earn on their assets (that they've put up as collateral to generate the oTokens) and buyers can purchase them on exchanges like 0x or Uniswap (using the latter to create a liquidity pool).

"Though derivatives markets comprise some of the most liquid markets in all of traditional finance, true derivatives markets are missing in DeFi. Options are amongst the most widely traded of derivative assets in traditional finance, with yearly exchange volume of more than $635 trillion (not including OTC options trading). Liquid options markets provide market participants with access to hedging, leverage, and financial insurance, making the development of such markets a prerequisite to DeFi’s maturation."

 — Convexity protocol white paper.

Beyond the primitive of fungible ERC-20 standardized options contracts, protective put strategies for deposit insurance are considered (as an extension of Opyn) — as means for, for example, protecting users of tokenized money markets like Compound against hacks and liquidity crises, or against stable coins like Dai crashing in value, etc. These oToken primitives allow users to hedge their risks, use as leverage, buy insurance, and also make bets on volatility (while also serving as oracles of volatility and risk in DeFi).

This is one of the first attempts to express options on Ethereum. Another protocol (Hegic), to have a quick look at in a later post, has also come to attention recently. Broadly, the main difference between the two seems to be that while Convexity is more technically flexible and general-purpose, Hegic appears to be more fintech and industry-oriented (in replicating traditional finance options in DeFi).