Draft Volatility Model
[Random Walk](https://texonom.com/random-walk-db1b5c7fa3e14a85b273f0f7d83efc19) [Volatility](https://texonom.com/volatility-242cf8faad7a404b833225f1b3bbe6f0) 


### 1년가
greek nu is drift
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Ff9ed0072-5d97-4ead-883e-839650d4def7%2FUntitled.png?table=block&id=d639e3be-b23e-4a5a-9c75-9302d3a41f94&cache=v2)



### Apply [Random Walk](https://texonom.com/random-walk-db1b5c7fa3e14a85b273f0f7d83efc19) $W$ to this
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F83de63cf-ac1d-48a8-a66c-8783573b0b89%2FUntitled.png?table=block&id=db00adb3-a449-4008-9e83-583815555b6e&cache=v2)

approximate return rate
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F6a25349a-d59d-45b0-9712-9464f2ea01eb%2FUntitled.png?table=block&id=f29f8de2-33a4-4aa4-ae1e-ac99026dfd89&cache=v2)


define $\mu$ and $\Delta W_t$
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F3f5ce927-0874-45e4-8bba-7642da777740%2FUntitled.png?table=block&id=2d43d4fa-4ab0-4192-bf71-a41405646531&cache=v2)
We can interpret $\mu$ related to [Market Draft](https://texonom.com/market-draft-2310fe564c7d4912b3dccf36ebe9865e) and $\sigma$ related to [Volatility](https://texonom.com/volatility-242cf8faad7a404b833225f1b3bbe6f0)  
즉 단위시간당 추세가 적용되고 변동성 random walk로 적
그런데 추세에도 변동성 제곱이 들어감 (1보다 작으므로 더작긴함)


### Make them infinity
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Ffd7478a4-4178-4fc9-abf0-eb5b70ad138e%2FUntitled.png?table=block&id=4828deb6-758f-4161-89af-ed5311efa518&cache=v2)






