### Key Differences:

**Implied Volatility (IV)**:

**What It Is**: IV is a measure derived from the price of an option, indicating the market’s expectations of the underlying asset’s future volatility.**Interpretation**: Higher IV suggests that the market expects more volatility (larger price swings) in the underlying asset, while lower IV indicates expectations of less volatility.**Use in Trading**: IV is used to price options and can give clues about the level of uncertainty or risk perceived by the market.

import scipy.optimize as opt

from math import log, sqrt, exp

from scipy.stats import norm## Black-Scholes Model to calculate the option price

def black_scholes_call(S, K, T, r, sigma):

d1 = (log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))

d2 = d1 – sigma * sqrt(T)

call_price = S * norm.cdf(d1) – K * exp(-r * T) * norm.cdf(d2)

return call_pricedef black_scholes_put(S, K, T, r, sigma):

d1 = (log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))

d2 = d1 – sigma * sqrt(T)

put_price = K * exp(-r * T) * norm.cdf(-d2) – S * norm.cdf(-d1)

return put_price## Function to calculate implied volatility

def implied_volatility(option_price, S, K, T, r, option_type=’call’):

def objective_function(sigma):

if option_type == ‘call’:

return black_scholes_call(S, K, T, r, sigma) – option_price

elif option_type == ‘put’:

return black_scholes_put(S, K, T, r, sigma) – option_price`# Debug: Print the value of the objective function at the bounds print(f"Objective function at sigma=0.0001: {objective_function(0.0001)}") print(f"Objective function at sigma=5.0: {objective_function(5.0)}") # Check if the function changes signs if objective_function(0.0001) * objective_function(5.0) > 0: raise ValueError("The objective function does not change signs over the interval.") # Using a numerical method to find the root, i.e., the implied volatility iv = opt.brentq(objective_function, 0.0001, 5.0) # Bound between 0.01% and 500% return iv`

## Example data

S_eth = 1850 # Current price of ETH in USD

S_sol = 25 # Current price of SOL in USD

S_btc = 30000 # Current price of BTC in USDK = 2000 # Strike price of the option

T = 30 / 365 # Time to expiration in years (e.g., 30 days)

r = 0.05 # Risk-free interest rate (5% annualized)

option_price_eth = 100 # Current price of the ETH option in USD

option_price_sol = 5 # Current price of the SOL option in USD

option_price_btc = 1200 # Current price of the BTC option in USD## Calculate Implied Volatility

try:

iv_eth = implied_volatility(option_price_eth, S_eth, K, T, r, option_type=’call’)

print(f”ETH Implied Volatility: {iv_eth:.2%}”)

except ValueError as e:

print(f”Error calculating IV for ETH: {e}”)try:

iv_sol = implied_volatility(option_price_sol, S_sol, K, T, r, option_type=’call’)

print(f”SOL Implied Volatility: {iv_sol:.2%}”)

except ValueError as e:

print(f”Error calculating IV for SOL: {e}”)try:

iv_btc = implied_volatility(option_price_btc, S_btc, K, T, r, option_type=’call’)

print(f”BTC Implied Volatility: {iv_btc:.2%}”)

except ValueError as e:

print(f”Error calculating IV for BTC: {e}”)

**Open Interest / Market Cap Ratio**:

**What It Is**: This ratio is calculated by dividing the open interest in derivatives (futures or options) by the market cap of the underlying asset.

**Interpretation**: It reflects the level of speculative interest in the asset relative to its total market value. A higher ratio may indicate more speculative trading relative to the asset’s size, while a lower ratio might indicate less speculative activity.

**Use in Trading**: This ratio is used to assess the scale of derivatives trading in relation to the size of the asset, which can offer insights into market sentiment and potential liquidity risks.

import requests

## Function to get market cap from CoinGecko API

def get_market_cap(coin_id):

url = f’https://api.coingecko.com/api/v3/coins/{coin_id}’

response = requests.get(url)

data = response.json()

market_cap = data[‘market_data’][‘market_cap’][‘usd’] # Market cap in USD

return market_cap## Function to get open interest from Binance Futures API

def get_open_interest(symbol):

url = ‘https://fapi.binance.com/fapi/v1/openInterest’

params = {‘symbol’: symbol}

response = requests.get(url, params=params)

data = response.json()

open_interest = float(data[‘openInterest’]) # Open interest in the base currency

return open_interest## Function to calculate the Open Interest / Market Cap Ratio

def calculate_oi_market_cap_ratio(coin_id, symbol):

market_cap = get_market_cap(coin_id)

open_interest = get_open_interest(symbol)

ratio = open_interest / market_cap

return ratio## Calculate and print the ratio for ETH

eth_ratio = calculate_oi_market_cap_ratio(‘ethereum’, ‘ETHUSDT’)

print(f”ETH Open Interest / Market Cap Ratio: {eth_ratio:.10f}”)## Calculate and print the ratio for SOL

sol_ratio = calculate_oi_market_cap_ratio(‘solana’, ‘SOLUSDT’)

print(f”SOL Open Interest / Market Cap Ratio: {sol_ratio:.10f}”)## Calculate and print the ratio for BTC

btc_ratio = calculate_oi_market_cap_ratio(‘bitcoin’, ‘BTCUSDT’)

print(f”BTC Open Interest / Market Cap Ratio: {btc_ratio:.10f}”)

### Summary:

**IV**is specifically related to the expected future volatility of an asset, as perceived by the market through the pricing of options.**Open Interest / Market Cap Ratio**gives a sense of the speculative interest relative to the size of the asset but does not directly measure volatility.

While both are useful in understanding market dynamics, they serve different purposes and are derived from different data points.

- DGM Bollinger Bands for Mean Reversion or Momentum Trending
- DGM SuperTrend, Open Interest, RSI
- Mean Reversion Strategy Using Z-Score on Premium Index
- Z-Score of Premium Index
- Moving Average Convergence Divergence (MACD) Histogram
- Mark Price (Implied Volatility – IV)

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