DERIVATIVES CHEAT SHEET

FORWARDS & FUTURES

Forward vs. Futures

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Pricing Formulas

No Income, No Storage: $$F_0 = S_0 \times (1 + r)^T$$

With Continuous Dividend Yield (q): $$F_0 = S_0 \times e^{(r-q)T}$$

Commodities (Storage Cost U, Convenience Yield y): $$F_0 = S_0 \times e^{(r+U-y)T}$$

Key Principle: Forward price = spot price + cost of carry

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Position Payoffs at Expiration

Long Forward: Payoff = $S_T - F_0$

• Profit if $S_T > F_0$; Loss if $S_T < F_0$

Short Forward: Payoff = $F_0 - S_T$

• Profit if $S_T < F_0$; Loss if $S_T > F_0$

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Futures Margin Rules

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Basis & Convergence

Basis = Spot – Futures Price

• Converges to zero at expiration (futures price → spot price)

• Basis risk: basis may not narrow as expected

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OPTIONS

Option Types & Moneyness

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Intrinsic & Time Value

Call Intrinsic Value: $\max(0, S - X)$ Put Intrinsic Value: $\max(0, X - S)$

Time Value = Premium – Intrinsic Value

• Decays to zero at expiration (theta decay)

• Highest for ATM options

• Buyer's max loss = premium paid; Seller's max profit = premium received

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Put-Call Parity (European, No Dividends)

$$C - P = S - PV(X)$$

where $PV(X) = \frac{X}{(1+r)^T}$

Rearranged: $C + PV(X) = P + S$

Violation → Arbitrage opportunity

Synthetic Positions:

• Long Call + Short Put = Long Forward

• Long Call + Long Put = Protective Collar (synthetic long stock + insurance)

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THE GREEKS (Option Sensitivity)

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Feature	Forward	Futures
Trading	OTC (private)	Exchange-traded
Customization	Fully customized	Standardized terms
Counterparty Risk	High (defaults accumulate)	Minimal (daily mark-to-market)
Settlement	At expiration only	Daily (mark-to-market)
Collateral	Negotiated/none initially	Margin required (initial + maintenance)
Price Discovery	Bilateral negotiation	Transparent market prices
Event	Action
Daily loss drops account below maintenance margin	Margin call required to restore to initial margin
Gain/loss settled daily	Eliminates counterparty risk
Account restricted if margin < maintenance	Must deposit or close position
Call	Put
ITM	$S > X$	$S < X$
ATM	$S ≈ X$	$S ≈ X$
OTM	$S < X$	$S > X$
Greek	Measures	Call	Put
Delta (δ)	Price change per $1 underlying move	0 to +1	0 to –1
Gamma (Γ)	Rate of delta change	Positive	Positive
Vega (ν)	Volatility sensitivity	Positive	Positive
Theta (θ)	Time decay (per day)	Negative (ITM/ATM)	Negative (ITM/ATM)
Rho (ρ)	Interest rate sensitivity	Positive	Negative

Delta Hedging: Hold option + short Δ shares → neutral to small underlying moves

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HIGH-YIELD DECISION RULES

When to Use Forwards vs. Futures?

• Forward: Customized exposure, acceptable counterparty, no margin pressure

• Futures: Standardized, leverage acceptable, need liquidity, want mark-to-market protection

Option Value Drivers:

• ↑ Volatility → ↑ Both call & put values (vega > 0)

• ↑ Time to expiration → ↑ Both call & put values (unless deep ITM put)

• ↑ Interest rates → ↑ Call, ↓ Put (rho effects)

• ↑ Stock price → ↑ Call, ↓ Put

Margin Call Trigger: Account value < Maintenance Margin → Deposit required

Intrinsic Value Always ≥ 0 (never negative)