II IntermediateWeek 22 • Lesson 63Duration: 45 min

DOCS Introduction to Financial Derivatives

Contracts built on top of other assets — and they run the financial world

Learning Objectives

•Understand what derivatives are and why they exist
•Know the main types: forwards, futures, options, swaps
•See how derivatives relate to quantitative trading

Explain Like I'm 5

A derivative is a contract whose value is derived from something else. A stock option's value depends on the stock price. A futures contract depends on the commodity price. They're called "derivatives" because they derive from an underlying asset. The concept is simple — they let you bet on price moves, hedge risk, or gain amplified exposure. What makes them fascinating is the math required to price them correctly.

Think of It This Way

Derivatives are like side bets at a sports game. The main "asset" is the game itself. But you can make side bets (derivatives) on: the final score (futures), whether a team scores more than 100 points (call option), the halftime lead (barrier option). The side bets derive their value from the game's outcome. Most of the financial action is in the side bets, not the game itself.

1Types of Derivatives

Forwards/Futures: Agreement to buy/sell an asset at a future date for a set price. - Forwards: private, customizable, counterparty risk - Futures: exchange-traded, standardized, margin system - Used for: hedging (farmers lock in crop prices) and speculation Options: RIGHT (not obligation) to buy/sell at a set price. - Call: right to BUY at strike price - Put: right to SELL at strike price - Premium: cost of buying the option - Used for: hedging, income generation, amplified directional bets Swaps: Exchange cash flows with counterparty. - Interest rate swap: fixed rate to floating rate - Currency swap: USD cash flows to EUR cash flows - Used for: managing interest rate and currency exposure The derivatives market is enormous — notional value exceeds $600 trillion. The actual stock market is small by comparison. These instruments are the backbone of global financial infrastructure.

2Why Quants Care About Derivatives

Derivatives are the original quantitative finance playground. Here's why: 1. They NEED math to price. You can't just "look at the chart" for options. You need stochastic calculus, probability theory, and numerical methods. This is why quantitative analysts exist as a profession. 2. Mispricings = tradeable edge. If you can price a derivative more accurately than the market, you can trade the difference. This is the original quant trade — and it still generates alpha today. 3. Surgical risk management. Derivatives let you hedge SPECIFIC risks with precision. Remove interest rate exposure with a swap. Get downside protection with a put. You choose exactly which risks to keep and which to offload. 4. Information gold mine. Option prices reveal what the market EXPECTS. Implied volatility tells you how scared people are. The term structure shows uncertainty over time. This is free information encoded in derivative prices. Even if you never trade options directly, understanding derivatives makes you a fundamentally better quant across every domain.

3How Derivatives Connect to Everything

Even if your production system trades FOREX spot and CFDs — not options — derivatives knowledge is still crucial: - VIX as a feature: The VIX is derived from S&P 500 option prices using a Black-Scholes-adjacent framework. Many quant systems use it as a regime indicator. - Futures basis: Some instruments are affected by futures roll dates and contango/backwardation dynamics. - Greeks for risk management: Delta and gamma concepts apply to ANY portfolio, not just options. - Implied vol as a signal: Option markets often price in information before spot markets react. Smart money tends to express views through options first. The quants who only understand spot trading and ignore derivatives are leaving genuine edge on the table. The options market is where informed money reveals its hand.

4Common Beginner Mistakes

Four mistakes that trip people up constantly: Mistake 1: Confusing futures with options. Futures OBLIGATE you. Options give you the RIGHT. If you sell a futures contract and price moves against you, you're on the hook. If you buy an option, worst case you lose the premium. Mistake 2: Ignoring counterparty risk. Forwards and OTC swaps have counterparty risk — the other side can default. Futures have clearing houses. This distinction matters significantly (ask anyone who was trading with Lehman Brothers in 2008). Mistake 3: Thinking derivatives are "dangerous." Derivatives aren't dangerous. Not understanding derivatives IS dangerous. A farmer hedging crop prices with futures is REDUCING risk. A fund buying puts for downside protection is being prudent. The danger comes from using them without understanding them. Mistake 4: Forgetting that premium is a real cost. Buying options costs money. If the stock goes sideways, your calls expire worthless. Theta decay eats your position every single day.

Long Call vs Long Put Payoff at Expiry (K=100, Premium=5)

Key Formulas

Put-Call Parity

Fundamental relationship between call (C), put (P), stock (S), strike (K), rate (r), and time (T). If this doesn't hold, there's a risk-free arbitrage opportunity.

Hands-On Code

Basic Derivative Payoffs

python

import numpy as np

def option_payoff(spot_prices, strike, premium, option_type='call', position='long'):
    """Compute option payoff at expiration."""
    if option_type == 'call':
        intrinsic = np.maximum(spot_prices - strike, 0)
    else:
        intrinsic = np.maximum(strike - spot_prices, 0)
    
    if position == 'long':
        payoff = intrinsic - premium
    else:  # short
        payoff = premium - intrinsic
    
    print(f"=== {position.upper()} {option_type.upper()} @ K={strike} ===")
    print(f"Premium paid: {premium:.2f}")
    print(f"Max loss: {premium:.2f}" if position == 'long' else f"Max loss: unlimited")
    
    return payoff

# Example: long call on SPX at strike 5000
# spot = np.linspace(4800, 5200, 100)
# payoff = option_payoff(spot, strike=5000, premium=50, option_type='call')

Computes option payoff at expiration for calls and puts, showing the asymmetric risk profile that makes derivatives powerful for risk management.

Knowledge Check

Q1.You buy a call option with strike $100 for a premium of $5. The stock ends at $108 at expiration. What's your profit?

Assignment

Plot payoff diagrams for: long call, short call, long put, short put, and a straddle (long call + long put at same strike). Understand how combining options creates complex payoff structures.

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