# Potion's Black-Scholes pricing system

Pricing the premium of an insurance product is tricky. Price it too high, and the buyer is over-paying for the insurance; price it too low, and the seller ends up losing all their collateral very quickly.

Potion uses an innovative approach to pricing, that finds fairest premium pricing possible for both buyer and seller.

In 1973, Fischer Black and Myron Scholes developed a mathematical approach to pricing options, on the basis of "risk-neutrality" for buyer and seller. In 1997 they would go on to win the Nobel prize in Economic Sciences for this contribution.

Here are the mechanics of the Black Scholes model:

As you can see, volatility is one of the inputs to the model. Intuitively, the price of an insurance should be higher, the higher the uncertainty about the future. This uncertainty is often expressed as "volatility".

Here's the catch with the BS-Model: at the time of pricing the option contract, parties can only check "

*historical volatility*", which may be very different to the*actual volatility*that will take place during the life of the contract.In practice, this means option sellers and buyers must "guess" what volatility may materialize in the future, and price their contracts accordingly. This volatility guess is called "implied volatility" - the market vote of what volatility will be in the future.

Potion's pricing system removes the need to "guess" what volatility will be - instead, it only fully settles the price of the premium at liquidation, on the basis of actual observed volatility (also referred to as

*realized volatility*). This is a key innovation, not available in classical fiat system.**Here's the process:**

- 1.
**At creation:**When the put potion is sold for the first time, buyer submits a "deposit" for the premium. This deposit is calculated such that it covers the worst volatility ever observed for the asset, plus a safety buffer. - 2.
**At liquidation**: When the put potion is exercised/expires, the Black-Scholes model is used to calculate the risk-neutral price that buyer/seller should have agreed.*REALIZED VOLATILITY*is used as an input to the model during the life of the contract, as opposed to implied volatility.

**This is better for the potion put seller**: If unexpected volatility spikes take place, sellers will be compensated for it, even if that couldn't have been predicted up-front.**This is better for the potion put buyer:**implied volatility is typically higher than realized volatility, meaning that buyers often over-pay for insurance, to compensate for the fact sellers are being cautious.

Using Black-Scholes "after the fact", means both parties get fairest possible premium - we call this perfect pricing 👌.