# 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.