# Options Premium Pricing & Casting costs

**Pricing Model:  xy=k**

OptionReserves(t)=x(t)

USDCReserves(t)=y(t)=120000+y.real(t) 

OptionPremium(t)=P(t)=y(t)/x(t)

x(t)\*y(t)=k=4.8\* 10^9 

P(0)=3 

x(0)=40000 

y(0)=120000

<figure><img src="https://lh3.googleusercontent.com/5JNQwSrkrdu8kodirHzWrQR9aeDCkzPVYEUybG3CumpIedeEmTEdxhyvzwn2yDLEPnxq-ppDhQ0rfX9jcOR6XeS7r2lgVYRMgN7gC5ycMIZ5C-y8rQqCChPaYrXpAsJgmiIVgY94ocI6j-ZsImVnAGcLKndDqKyFoitNsJ4MuZDBWG6hgkam0zojGvBqyw" alt=""><figcaption></figcaption></figure>

**Calculate the price to buy an option**

δx *<mark style="color:yellow;"># The number of options purchased by the user</mark>*

δy  *<mark style="color:yellow;"># The amount of USDC paid by the user to purchase the option</mark>*

(x-δx)(y+δy)=x\*y=k

δy = x*y / (x-δx) - y = 4.8*10^9 / (x-δx)-y

\
The total number of each team’s Options cards is 40,000, and the overall cost of purchasing the Option is from **3 USDC upwards**. According to the programming of NFTEA’s casting system, the more team Options cards are purchased, the higher the cost will become.

Among them, the cost of the first 10,000 team Options cards is about 3–4 USDC; the cost of the 10,000–20,000th team Options cards is about 4–12 USDC; the cost of the 20,000–30,000th team Options cards is about 12–48 USDC.

With this model, we see that the earlier you buy the lower the prices are, and the price change (increase in price) for earlier purchases is small; and as the number of option purchases increases, the subsequent growth in cost starts to shows bigger changes, i.e., as more and more options representing a single team are purchased, the price grows faster and faster. This is an AMM mechanism using NFT options whose purchase cost is determined by supply alone with no human intervention, which fully reflects the gameplay.


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