The Full Derivatives Crash Course: Part 1 – First Principles

Introducing the series

Derivatives sit at the heart of modern finance. They’re the reason risk can move from one balance sheet to another. Every structured product, swap, or exotic option ultimately rests on the same foundation: a relationship between a spot price and a future price, linked by no-arbitrage.

Before we reach option pricing or swaps, we need this base. Once you understand how a forward price is built, the rest of the derivatives world becomes pattern recognition.

Part 1’s Learning Outcomes

In the first part of this course, we aim to underscore the key principles of learning derivatives academically, hence setting everyone up for learning about the interesting yet complicated material later on. So, today we aim to:

• Explain what derivatives are and why they exist.
• Distinguish between OTC markets and exchange-traded markets.
• Distinguish between forwards and futures.
• Define and learn to use spot–forward parity under different income/yield setups.
• Interpret the basis, convergence, and the role of the clearing house & margins.

So without further ado, let’s look under the derivative microscope…

What is a Derivative?

A derivative is a financial contract whose value is derived from an underlying asset, be it equity, a bond, a commodity, an index, an interest rate, or even weather. Its economic purpose is simple but powerful:

• Risk transfer: allows one party to offload unwanted exposure.
• Price discovery: reveals the market’s consensus on future values.
• Financing efficiency: enables synthetic positions without directly owning the asset.

In essence, derivatives make markets more complete, they allow risks to be priced, traded, and shared.

Market structure

Two architectures dominate: exchange-traded and OTC (over-the-counter).

Exchange-traded derivatives are standardised. They trade on organised exchanges with central clearing and daily margining. Counterparty risk is minimal because the clearing house stands in the middle of every trade.

OTC derivatives are customised bilateral contracts, negotiated privately. They allow flexibility in terms, size and settlement, but they expose each counterparty to the other’s credit risk. Post-2008 reforms have pushed much of this market toward central clearing as well.

Futures vs Forwards

They sound similar but structure and risk differ.

The result: forwards are used by corporates and institutions needing precision; futures dominate where liquidity, transparency, and leverage matter.

Core Definitions

• Spot price (S₀): current market price of the underlying.
• Futures/forward price (F₀): price agreed today for delivery at time T.
• Basis (b = S − F): difference between spot and futures; reflects carry costs and convergence.
• Open interest: number of outstanding contracts.
• Settlement price: official closing price used for margining.
• Volume: number of contracts traded during a session.

No-arbitrage: the spot–forward link

At the centre of derivatives pricing lies one rule — no arbitrage.
If two strategies create the same cash flows, they must have the same price.

(a) Base case — no income

Forward price = Spot compounded at the risk-free rate
Formula: F₀ = S₀ × e^(r × T)

(b) Asset with known cash income (I)

Forward price = (Spot − Present Value of income) compounded at r
Formula: F₀ = (S₀ − I) × e^(r × T)

(c) Asset with a known continuous yield (q)

Forward price = Spot adjusted for yield
Formula: F₀ = S₀ × e^((r − q) × T)

These versions describe equities with dividends, bonds with coupons, or commodities with storage yields.
Even when short-selling is restricted, parity still holds as long as investors can replicate the payoff through borrowing and lending.

Patterns and Spreads

Futures prices across maturities form a term structure.

• Contango (normal market): longer-dated futures trade above spot.
• Backwardation (inverted market): longer-dated futures trade below spot.

Consistency between contracts of different maturities comes from the carry relationship:
F(T₂) = F(T₁) × e^((r − q) × (T₂ − T₁))

This ensures that pricing remains coherent across delivery months.

Futures mechanics and profit/loss

Futures profits and losses are settled each day rather than at maturity.

• Initial margin: deposit required to open a position.
• Maintenance margin: minimum balance that must be maintained.
• Margin call: notice to top up funds if losses reduce the account below the maintenance level.

Profit and loss at expiry:

• Long position: P/L = Fₜ − F₀
• Short position: P/L = F₀ − Fₜ

As expiry approaches, the futures and spot prices converge. Any gap would invite risk-free arbitrage until the difference disappears.

Orders and Clearing

Common order types:

• Market order: executes immediately at the best available price.
• Limit order: executes only at a specified price or better.
• Stop / if-touched order: activates once a target price is reached.

Behind every trade sits the clearing house. It becomes the buyer to every seller and the seller to every buyer, guaranteeing performance and managing margin flows. This central counterparty structure nearly eliminates default risk.

Why Parity Matters

Spot–forward parity keeps prices anchored to economic reality.
If futures prices drift too high, arbitrageurs sell the futures and buy the underlying; if too low, they do the reverse. Their activity restores alignment.

Every derivative model, from swaps to Black-Scholes, relies on this same foundation: identical cash flows must cost the same.

Next Up

In Blog 2 – Hedging with Futures & Interest Rate Swaps, we’ll look at how traders and firms use these instruments to manage exposure, stabilise cash flows, and transform risk into something measurable.