> For the complete documentation index, see [llms.txt](https://docs.pancakeswap.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.pancakeswap.finance/trade/perpetual-trading/perpetual-trading-v2/madbtcusd/madbtcusd-faq.md).
# MADBTCUSD FAQ
### How is MADBTCUSD Index Calculated?
MADBTCUSD is calculated based on the following formula:
**MADBTCUSD Index**
$$
\begin{align\*}
\text{drift} &= \left( \frac{\text{btcCurrentPrice} - 1}{\text{btcLastSecondPrice}} \right) \times 5 \\
\\
\sigma &= \frac{\text{expectedvol}}{\sqrt{3600 \times 24 \times 365}} \\
\\
norm &= \text{norminv}(\text{Random}, 0, 1) \\
\\
S\_{n+1} &= S\_{n} \times e^{\left\[\left(\text{drift} - \frac{\sigma^2}{2}\right) \times \text{dt} + \sigma \times \sqrt{\text{dt}} \times norm\right]}
\end{align\*}
$$
where:
* Initial Sn=1000
* dt=1
* expected vol：100%(expected vol is the expected time volatility of the MADBTC)
* the "**Random number**" is calculated based on the current **BTC price with 8 decimal places of precision**
**Calculation of Random Number:**
```python
import hashlib
from decimal import Decimal
# Assume the current price of Bitcoin is 48923.56789101
bitcoin_price = Decimal("48923.56789101")
# Calculate the SHA-256 hash of the Bitcoin price
price_hash = hashlib.sha256(str(bitcoin_price).encode('utf-8')).hexdigest()
# Extract the first 8 hexadecimal numbers from the hash
hash_substring = price_hash[:8]
# Converts a hexadecimal string to an integer
hash_integer = int(hash_substring, 16)
# Divide the integer by 4294967296 (the decimal number corresponding to the hexadecimal number FFFFFFFF) to get a num
random_number = hash_integer / 4294967296
# Print the random number
print(random_number)
```
If the random number determined is 0, it will be recalculated again
### Where can I cross-verify the BTC and MADBTCUSD historical price?
The BTC and MADBTCUSD price feed can be found here:
[BTCUSD](https://www.apollox.finance/bapi/futures/v1/public/future/apx/V2MarkPriceKline?symbol=BTCUSD\&limit=1800)
[MADBTCUSD](https://www.apollox.finance/bapi/futures/v1/public/future/apx/V2MarkPriceKline?symbol=MADBTCUSD\&limit=1800)
### Historical backtest data of BTC & MADBTC
To cross-verify the BTC & MADBTC historical prices, we've provided a backtest graph below.
---
# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.
## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation by asking a question.
Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters:
```
GET https://docs.pancakeswap.finance/trade/perpetual-trading/perpetual-trading-v2/madbtcusd/madbtcusd-faq.md?ask=&goal=
```
`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.
Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.
