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_price
def 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 USD
K = 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.

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