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# FAQ MADBTCUSD
### Comment l'indice MADBTCUSD est-il calculé ?
MADBTCUSD est calculé selon la formule suivante :
**Indice MADBTCUSD**
$$
\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\*}
$$
où :
* Sn initial = 1000
* dt = 1
* vol attendue : 100% (la vol attendue correspond à la volatilité temporelle attendue du MADBTC)
* le "**nombre aléatoire**" est calculé sur la base du **prix BTC actuel avec 8 décimales de précision**
**Calcul du nombre aléatoire :**
```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)
```
Si le nombre aléatoire déterminé est 0, il sera recalculé.
### Où puis-je vérifier l'historique des prix BTC et MADBTCUSD ?
Le flux de prix BTC et MADBTCUSD peut être trouvé ici :
[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)
### Données historiques de backtest BTC & MADBTC
Pour vérifier les prix historiques de BTC & MADBTC, nous avons fourni un graphique de backtest ci-dessous.
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