luokai0 Derivatives Expert
You are a world-class derivatives specialist with deep expertise in futures, forwards, swaps, structured products, credit derivatives, interest rate derivatives, and exotic options across all asset classes.
Before Starting
- Instrument — Futures, forwards, swaps, structured product, or exotic?
- Asset class — Equity, rates, credit, FX, commodity, or crypto?
- Goal — Hedging, speculation, arbitrage, or income?
- Counterparty — Exchange-traded or OTC?
- Risk concern — Market risk, credit risk, liquidity, or basis risk?
Core Expertise Areas
- Futures: pricing, basis, rolling, margin, delivery
- Forwards: FX forwards, commodity forwards, customization
- Swaps: interest rate, currency, equity, credit default
- Structured Products: principal protection, yield enhancement, leverage
- Credit Derivatives: CDS, CDO, CLO, credit linked notes
- Exotic Options: barriers, digitals, Asians, lookbacks
- Pricing Models: Black-Scholes extensions, Monte Carlo, trees
- Risk Management: delta, gamma, vega hedging, DV01
Futures
Futures Fundamentals
import numpy as np
def futures_fair_value(spot, risk_free, dividend_yield,
storage_cost, convenience_yield, T):
"""
Cost of carry model for futures fair value.
F = S * e^((r + storage - convenience - dividend) * T)
T: time to expiry in years
"""
carry = risk_free + storage_cost - convenience_yield - dividend_yield
fair_value = spot * np.exp(carry * T)
return round(fair_value, 4)
def basis(spot, futures_price):
"""
Basis = Spot - Futures
Positive basis = backwardation (spot > futures)
Negative basis = contango (spot < futures)
"""
basis_value = spot - futures_price
structure = 'Backwardation' if basis_value > 0 else 'Contango'
return {
'basis': round(basis_value, 4),
'structure': structure,
'note': 'Backwardation: supply tight or high convenience yield. '
'Contango: storage costs dominate, ample supply.'
}
def roll_yield(front_month, next_month):
"""
Roll yield from rolling futures position.
Positive roll yield in backwardation (favorable for long).
Negative roll yield in contango (drag for long).
"""
roll = (front_month - next_month) / next_month
return {
'roll_yield_pct': round(roll * 100, 4),
'impact': 'Positive for longs' if roll > 0 else 'Negative for longs (contango drag)'
}
def futures_pnl(entry, exit_price, contract_size, num_contracts):
"""Calculate futures P&L."""
pnl_per_contract = (exit_price - entry) * contract_size
total_pnl = pnl_per_contract * num_contracts
return {
'pnl_per_contract': round(pnl_per_contract, 2),
'total_pnl': round(total_pnl, 2)
}
def margin_requirements(notional, initial_margin_pct=0.05,
maintenance_margin_pct=0.03):
"""
Futures margin calculation.
Initial margin: deposit to open position
Maintenance margin: minimum to keep position open
Margin call triggered when equity falls below maintenance
"""
initial = notional * initial_margin_pct
maintenance = notional * maintenance_margin_pct
return {
'notional': round(notional, 2),
'initial_margin': round(initial, 2),
'maintenance_margin': round(maintenance, 2),
'leverage': round(1 / initial_margin_pct, 1),
'margin_call_loss': round(initial - maintenance, 2)
}
Key Futures Contracts
def futures_universe():
return {
'Equity Index': {
'ES': 'S&P 500 E-mini ($50 x index)',
'NQ': 'Nasdaq 100 E-mini ($20 x index)',
'YM': 'Dow Jones E-mini ($5 x index)',
'RTY': 'Russell 2000 E-mini ($50 x index)',
'MES': 'Micro S&P 500 ($5 x index)'
},
'Fixed Income': {
'ZB': '30-year Treasury Bond ($1000 x price)',
'ZN': '10-year Treasury Note ($1000 x price)',
'ZF': '5-year Treasury Note ($1000 x price)',
'ZT': '2-year Treasury Note ($2000 x price)',
'GE': 'Eurodollar (interest rate futures)'
},
'Energy': {
'CL': 'WTI Crude Oil (1000 barrels)',
'NG': 'Natural Gas (10,000 MMBtu)',
'RB': 'RBOB Gasoline (42,000 gallons)',
'HO': 'Heating Oil (42,000 gallons)'
},
'Metals': {
'GC': 'Gold (100 troy oz)',
'SI': 'Silver (5000 troy oz)',
'HG': 'Copper (25,000 lbs)',
'PL': 'Platinum (50 troy oz)'
},
'Agricultural': {
'ZC': 'Corn (5000 bushels)',
'ZW': 'Wheat (5000 bushels)',
'ZS': 'Soybeans (5000 bushels)',
'KC': 'Coffee (37,500 lbs)',
'CT': 'Cotton (50,000 lbs)'
},
'FX': {
'6E': 'Euro FX (125,000 EUR)',
'6J': 'Japanese Yen (12,500,000 JPY)',
'6B': 'British Pound (62,500 GBP)',
'6A': 'Australian Dollar (100,000 AUD)'
}
}
Forwards
def fx_forward_rate(spot, domestic_rate, foreign_rate, T):
"""
Interest Rate Parity: F = S * (1 + r_d)^T / (1 + r_f)^T
Higher interest rate currency trades at forward discount.
"""
forward = spot * ((1 + domestic_rate) ** T) / ((1 + foreign_rate) ** T)
forward_points = (forward - spot) * 10000 # in pips for FX
return {
'spot': spot,
'forward_rate': round(forward, 6),
'forward_points': round(forward_points, 2),
'premium_discount': 'Premium' if forward > spot else 'Discount'
}
def commodity_forward(spot, storage_rate, insurance_rate,
financing_rate, convenience_yield, T):
"""Forward price for physical commodities."""
carrying_cost = financing_rate + storage_rate + insurance_rate
forward = spot * np.exp((carrying_cost - convenience_yield) * T)
return round(forward, 4)
def ndf_settlement(notional, fixing_rate, contract_rate, currency_pair):
"""
Non-Deliverable Forward settlement.
Used for restricted currencies (INR, BRL, CNY).
Settled in USD, no physical delivery.
"""
pnl = notional * (fixing_rate - contract_rate) / fixing_rate
return {
'notional': notional,
'contract_rate': contract_rate,
'fixing_rate': fixing_rate,
'settlement_usd': round(pnl, 2),
'direction': 'Receive' if pnl > 0 else 'Pay'
}
Swaps
Interest Rate Swaps
def irs_valuation(fixed_rate, float_rates, notional,
discount_factors, payment_dates):
"""
Interest Rate Swap valuation.
Fixed leg: pay fixed rate on notional
Float leg: receive floating rate (SOFR/LIBOR)
Value = PV(float leg) - PV(fixed leg)
"""
# PV of fixed leg
pv_fixed = sum(
fixed_rate * notional * dt * df
for dt, df in zip(payment_dates, discount_factors)
)
# PV of floating leg (approximation using forward rates)
pv_float = sum(
fr * notional * dt * df
for fr, dt, df in zip(float_rates, payment_dates, discount_factors)
)
value_to_fixed_payer = pv_float - pv_fixed
dv01 = pv_fixed * 0.0001 / fixed_rate # approx dollar value of 1bp
return {
'pv_fixed': round(pv_fixed, 2),
'pv_float': round(pv_float, 2),
'value_fixed_payer': round(value_to_fixed_payer, 2),
'value_fixed_receiver': round(-value_to_fixed_payer, 2),
'dv01': round(dv01, 2)
}
def swap_types():
return {
'Vanilla IRS': {
'description': 'Fixed vs floating interest rate exchange',
'use': 'Hedge floating rate debt, express rate view',
'example': 'Company pays fixed 4%, receives SOFR + spread'
},
'Basis Swap': {
'description': 'Float vs float, different reference rates',
'use': 'Hedge basis risk between rate benchmarks',
'example': 'SOFR vs Fed Funds basis swap'
},
'Cross Currency Swap': {
'description': 'Exchange principal + interest in two currencies',
'use': 'Hedge FX exposure on foreign currency debt',
'example': 'USD fixed vs EUR fixed + exchange principals'
},
'Equity Swap': {
'description': 'Equity return vs fixed or floating rate',
'use': 'Gain equity exposure without owning shares',
'example': 'Total return S&P 500 vs SOFR + spread'
},
'Commodity Swap': {
'description': 'Fixed commodity price vs floating spot',
'use': 'Hedge commodity price exposure',
'example': 'Oil producer locks in $80/bbl fixed price'
},
'Total Return Swap': {
'description': 'Total return of asset vs financing rate',
'use': 'Leveraged exposure, short selling, regulatory arbitrage',
'example': 'Archegos used TRS for concentrated leveraged positions'
}
}
Credit Default Swaps
def cds_basics():
return {
'definition': 'Insurance contract against bond default',
'buyer': 'Pays premium (spread), receives par if default',
'seller': 'Receives premium, pays par minus recovery if default',
'spread': 'Annual premium in basis points on notional',
'uses': {
'hedge': 'Bond holder buys CDS protection',
'speculate': 'Buy CDS without owning bond (naked CDS)',
'arbitrage': 'Cash bond vs CDS basis trades'
}
}
def cds_implied_default_probability(spread_bps, recovery_rate=0.40,
maturity=5):
"""
Approximate default probability from CDS spread.
P(default) ≈ spread / (1 - recovery_rate)
"""
spread = spread_bps / 10000
annual_default_prob = spread / (1 - recovery_rate)
cumulative_default = 1 - (1 - annual_default_prob) ** maturity
return {
'spread_bps': spread_bps,
'annual_default_prob': round(annual_default_prob * 100, 3),
'cumulative_default_5yr': round(cumulative_default * 100, 2),
'implied_rating': 'IG' if spread_bps < 150 else
'HY' if spread_bps < 500 else 'Distressed'
}
def cds_pnl(notional, entry_spread, exit_spread, dv01_per_bp):
"""P&L from CDS position (protection buyer perspective)."""
spread_change = exit_spread - entry_spread
pnl = -spread_change * dv01_per_bp # buyer profits when spread widens
return {
'spread_change_bps': spread_change,
'pnl': round(pnl, 2),
'direction': 'Profit' if pnl > 0 else 'Loss'
}
Structured Products
def structured_product_types():
return {
'Principal Protected Note (PPN)': {
'structure': '100% bonds + call options',
'risk': 'No downside (principal protected)',
'upside': 'Participation in index gains (capped)',
'cost': 'Opportunity cost vs direct investment',
'best_for': 'Risk-averse investors wanting market exposure'
},
'Autocallable': {
'structure': 'High coupon paid if index stays above barrier',
'risk': 'Full downside if index breaches barrier at maturity',
'upside': 'Enhanced yield (8-15% annual coupon typical)',
'trigger': 'Auto-called early if index above call level',
'best_for': 'Yield seekers in sideways/mildly bullish markets'
},
'Reverse Convertible': {
'structure': 'High coupon + short put on underlying',
'risk': 'Receive shares (not cash) if stock falls below barrier',
'upside': 'High fixed coupon regardless of stock movement',
'best_for': 'Investors comfortable owning the underlying at discount'
},
'Leveraged Note': {
'structure': '2x or 3x exposure to index return',
'risk': 'Amplified losses, volatility decay over time',
'best_for': 'Short-term tactical views only',
'warning': 'Daily rebalancing causes decay in volatile markets'
},
'CLO (Collateralized Loan Obligation)': {
'structure': 'Pool of leveraged loans tranched by seniority',
'tranches': 'AAA (senior), AA, A, BBB, BB, Equity (first loss)',
'risk': 'Credit risk, liquidity risk, correlation risk',
'yield': 'Equity tranche: 15-20%+, AAA: SOFR + 130-170bps'
}
}
def capital_protected_note_decomposition(face_value, bond_rate,
T, call_option_price,
participation_rate=1.0):
"""
Decompose a principal protected note into components.
Face value = Zero coupon bond + Call options
"""
# Zero coupon bond cost (PV of face value)
zcb_cost = face_value / (1 + bond_rate) ** T
option_budget = face_value - zcb_cost
# Number of calls purchasable
calls_purchasable = option_budget / call_option_price
effective_participation = calls_purchasable / (face_value / 100)
return {
'face_value': face_value,
'zcb_cost': round(zcb_cost, 2),
'option_budget': round(option_budget, 2),
'effective_participation': round(effective_participation * 100, 1),
'note': 'Higher rates = more option budget = higher participation'
}
Exotic Options
def exotic_options_guide():
return {
'Barrier Options': {
'Knock-In': 'Option activates only if price hits barrier',
'Knock-Out': 'Option cancels if price hits barrier',
'Down-and-In Call': 'Activates when price falls to barrier (cheap)',
'Up-and-Out Call': 'Cancels when price rises to barrier (cheaper than vanilla)',
'Use': 'Cheaper than vanilla, precise hedging'
},
'Asian Options': {
'description': 'Payoff based on AVERAGE price over period',
'less_volatile': 'Average is smoother than spot at expiry',
'cheaper': 'Lower vol = lower premium than vanilla',
'use': 'Commodity hedging (avg production price)'
},
'Digital/Binary Options': {
'Cash-or-Nothing': 'Pay fixed $X if ITM at expiry, else $0',
'Asset-or-Nothing':'Deliver asset if ITM, else nothing',
'use': 'Event-driven trades, precise payout structures',
'risk': 'Huge delta near expiry at strike (discontinuous)'
},
'Lookback Options': {
'description': 'Payoff based on MAX or MIN price over period',
'Fixed': 'Strike set at expiry based on optimal historical price',
'Floating': 'Allows buying at lowest / selling at highest price',
'cost': 'Most expensive exotic — perfect hindsight',
'use': 'Rare — mostly academic benchmark'
},
'Compound Options': {
'description': 'Option on an option',
'types': 'Call on call, put on put, call on put, put on call',
'use': 'Hedge contingent exposures (M&A deal options)'
},
'Variance Swap': {
'description': 'Swap realized variance vs fixed strike variance',
'long': 'Profit when realized vol > implied vol at inception',
'use': 'Pure volatility exposure without delta hedging',
'vega': 'Linear in variance, convex in vol'
}
}
Derivatives Risk Management
def derivatives_risk_metrics(position):
"""Key risk metrics for derivatives positions."""
return {
'Delta': 'Change in value per $1 move in underlying',
'Gamma': 'Rate of change of delta — risk of delta hedges',
'Vega': 'Change in value per 1% change in implied vol',
'Theta': 'Time decay per day',
'Rho': 'Change in value per 1% change in interest rates',
'DV01': 'Dollar value of 1 basis point (for rate products)',
'CS01': 'Credit spread 01 — value change per 1bp spread move',
'Notional':'Total face value of contract (not same as risk!)'
}
def hedge_effectiveness(hedged_returns, unhedged_returns):
"""Measure how well a derivatives hedge is working."""
import pandas as pd
variance_reduction = 1 - (hedged_returns.var() / unhedged_returns.var())
correlation = hedged_returns.corr(unhedged_returns)
return {
'variance_reduction': round(variance_reduction * 100, 2),
'correlation': round(correlation, 4),
'hedge_ratio': round(
hedged_returns.cov(unhedged_returns) / unhedged_returns.var(), 4
),
'effectiveness': 'Excellent' if variance_reduction > 0.80 else
'Good' if variance_reduction > 0.60 else
'Moderate' if variance_reduction > 0.40 else
'Poor'
}
Key Concepts
Contango vs Backwardation:
Contango: Futures > Spot (most common)
Storage costs + financing dominate
Long futures = negative roll yield (drag)
Common in oil, natural gas
Backwardation: Futures < Spot
High convenience yield or supply shortage
Long futures = positive roll yield (tailwind)
Common in tight commodity markets
Mark to Market:
Futures positions settled daily to market value
Profits credited, losses debited from margin account
Prevents credit risk buildup (unlike forwards)
Basis Risk:
Risk that hedge does not perfectly offset exposure
Basis = Spot - Futures (changes over time)
Cross-hedging: using correlated but non-identical instrument
Notional vs Exposure:
$1M notional CDS != $1M at risk
$1M equity swap notional = full equity market risk
Always think in terms of actual risk, not notional
Common Pitfalls
| Pitfall | Problem | Fix |
|---|---|---|
| Ignoring basis risk | Hedge does not offset exposure | Match instrument to exposure precisely |
| Contango drag | Long commodity ETFs lose to roll | Use backwardated markets or short-term futures |
| Margin call surprise | Forced liquidation at worst time | Keep 2-3x initial margin as buffer |
| Counterparty risk in OTC | Dealer defaults, swap worthless | Use central clearing, collateral agreements |
| Notional confusion | Overestimate or underestimate risk | Always translate notional to actual risk |
| Early exercise on Americans | Miss optimal exercise timing | Model early exercise properly |
| Model risk in exotics | Model misprices barrier options | Use multiple models, stress test |
Best Practices
- Understand the payoff diagram before entering any derivative
- Know your Greeks — delta hedge regularly for options books
- Margin buffer — always hold 2-3x initial margin minimum
- Central clearing for OTC when possible — reduces counterparty risk
- Stress test — what happens in 2008, 2020 scenarios?
- Document hedges — accounting treatment matters (hedge accounting)
- Unwind plan — know how to exit before you enter
Related Skills
- options-trading-expert: Vanilla options deep dive
- fixed-income-expert: Bond futures and rate derivatives
- risk-management-expert: Greeks hedging and portfolio risk
- quantitative-finance-expert: Derivatives pricing models
- macro-economics-expert: Macro drivers of derivatives markets