The Greeks and Option Risk Management › Option Portfolio Risk Reports
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In practice, we work with entire portfolios of options rather than individual positions. A typical risk report aggregates Greeks across all positions. In the code below, we define a portfolio of mixed positions, calculate the Greeks for each, and sum them to determine the net portfolio exposure:
# Sample portfolio of options on the same underlying
portfolio = [
{"type": "call", "K": 95, "T": 0.25, "position": 50}, # Long 50 ITM calls
{"type": "put", "K": 100, "T": 0.25, "position": -30}, # Short 30 ATM puts
{"type": "call", "K": 105, "T": 0.5, "position": 100}, # Long 100 OTM calls
{"type": "put", "K": 95, "T": 0.5, "position": 25}, # Long 25 OTM puts
]
S, r, sigma = 100, 0.05, 0.20
# Calculate portfolio Greeks
portfolio_greeks = {"Delta": 0, "Gamma": 0, "Theta": 0, "Vega": 0, "Rho": 0}
portfolio_details = []
for pos in portfolio:
opt = BlackScholesGreeks(S, pos["K"], pos["T"], r, sigma, pos["type"])
n = pos["position"]
details = {
"Description": f"{pos['type'].upper()} K={pos['K']} T={pos['T']}y",
"Position": n,
"Price": opt.price(),
"Delta": n * opt.delta(),
"Gamma": n * opt.gamma(),
"Theta": n * opt.theta() / 365,
"Vega": n * opt.vega() / 100,
}
portfolio_details.append(details)
portfolio_greeks["Delta"] += details["Delta"]
portfolio_greeks["Gamma"] += details["Gamma"]
portfolio_greeks["Theta"] += details["Theta"]
portfolio_greeks["Vega"] += details["Vega"]Option Portfolio Risk Report =========================================================================== Underlying: $100 | Vol: 20% | Rate: 5% =========================================================================== Position Qty Delta Gamma Theta Vega --------------------------------------------------------------------------- CALL K=95 T=0.25y 50 37.71 1.5744 -1.33 7.87 PUT K=100 T=0.25y -30 12.92 -1.1786 0.46 -5.89 CALL K=105 T=0.5y 100 46.12 2.8076 -2.11 28.08 PUT K=95 T=0.5y 25 -6.77 0.5854 -0.22 5.85 --------------------------------------------------------------------------- PORTFOLIO TOTAL 89.97 3.7888 -3.20 35.91
This type of report allows you to quickly understand your exposures and decide whether to hedge. The portfolio above is long delta, meaning it benefits from rising stock prices (gaining approximately the delta amount for a $1 increase. It is also long gamma and vega, meaning the position value increases with both large market moves and rising volatility. However, these benefits come at a cost: the negative theta indicates the portfolio loses value daily due to time decay.
