What is a derivative contract?
A derivative is a contract. Its value comes from another thing, called the underlying. The underlying can be a share, a stock index, a currency, gold or wheat.
There are four main kinds: forwards, futures, options and swaps. People use them for three jobs:
- Hedging: cutting risk, like a farmer fixing a selling price.
- Speculation: betting on where the price will go.
- Arbitrage: earning a small, safe profit from two prices that do not match.
Forwards and futures: how the mechanism works
A forward is a private deal between two people. They agree on a price today for a trade on a later date. There is a risk the other side does not pay (counterparty risk).
A futures contract fixes these problems:
- It is standard: fixed lot size, fixed expiry date, traded on an exchange.
- A clearing house stands between buyer and seller and guarantees the trade.
- Both sides deposit an initial margin (a part of the contract value, often 10–20%).
- Each day the contract is marked to market: the day’s gain is added to one account and the loss taken from the other. If a balance falls below the maintenance margin, a margin call asks for more money.
- Most futures are closed before expiry. Some are settled in cash, some by delivery.
Long and short
The buyer is long (gains if the price rises). The seller is short (gains if the price falls). Payoff of long futures = Price at expiry − Futures price.
Options: calls, puts and payoffs
An option gives the buyer a right, not a duty. The buyer pays a premium to the seller (the writer).
- Call option: the right to buy at the strike price.
- Put option: the right to sell at the strike price.
A European option can be used only on the expiry date. An American option can be used any day until expiry.
Payoffs at expiry (per unit)
- Call buyer: max(S − K, 0) − premium. Break-even = K + premium.
- Put buyer: max(K − S, 0) − premium. Break-even = K − premium.
- The buyer’s biggest loss is the premium. The writer’s loss can be very large, so the writer must keep margin.
Moneyness
A call is in the money when S > K, at the money when S = K, and out of the money when S < K. For a put it is the other way round.
Pricing futures and options
Futures price ≈ spot price + cost of carry. Holding the real thing until later costs interest (and storage), and you may lose dividends. A simple form: F = S × (1 + r × t) − income, where r is the yearly interest rate and t is time in years.
Option premium = intrinsic value + time value.
- Intrinsic value = what you would get if you used it now: max(S − K, 0) for a call, max(K − S, 0) for a put.
- Time value = the extra people pay because the price may still move in your favour. It shrinks to zero at expiry (time decay).
A premium is higher when the price swings a lot (high volatility), when more time is left, and (for calls) when interest rates are higher. Experts use models such as Black–Scholes or the binomial tree; at school level you only need the ideas above.
Risks
Derivatives use leverage: a small margin controls a big contract, so losses grow fast. Most new traders lose money, so regulators warn retail investors.
Try it: hedge a farmer
Take a farmer who will sell 10 bags of wheat in 3 months. Today the futures price is 100 per bag. Write two cases: price later 80 and price later 120. Work out (1) money from selling wheat, (2) gain or loss on a short futures position, (3) total. You will find the total is 1,000 in both cases. That is a perfect hedge. Then try it in the 3D: choose “Short futures” and move the price.
Key formulas and definitions
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Worked examples
1. You buy one futures contract of 50 units at 200. At expiry the price is 212. Find your profit.
Gain per unit = 212 − 200 = 12. Total = 12 × 50 = 600.
2. A call has strike 100 and premium 5. Find the profit per unit if the expiry price is 112, and if it is 90.
At 112: max(112 − 100, 0) − 5 = 12 − 5 = 7 profit. At 90: max(90 − 100, 0) − 5 = 0 − 5 = −5, a loss of only the premium.
3. A put has strike 500 and premium 20. Find the break-even and the profit at expiry price 450.
Break-even = 500 − 20 = 480. At 450: max(500 − 450, 0) − 20 = 50 − 20 = 30 profit per unit.
4. Spot price is 1,000, yearly interest rate is 8%, time to expiry is 3 months, no dividend. Estimate the futures price.
t = 3/12 = 0.25. F = 1,000 × (1 + 0.08 × 0.25) = 1,000 × 1.02 = 1,020.
5. A share trades at 260. A call with strike 250 costs 18. Split the premium.
Intrinsic value = max(260 − 250, 0) = 10. Time value = 18 − 10 = 8.
6. Initial margin is 10,000 and maintenance margin is 7,500 on a long futures of 100 units bought at 400. On day 1 the price is 390; on day 2 it is 370. When is there a margin call and how much must be paid?
Day 1: loss = 10 × 100 = 1,000, balance = 9,000 (above 7,500, no call). Day 2: loss = 20 × 100 = 2,000, balance = 7,000 (below 7,500). Margin call: top up back to the initial margin, 10,000 − 7,000 = 3,000.
Common mistakes
- Thinking an option buyer must buy or sell. The buyer has a right, not a duty; only the writer has a duty.
- Forgetting the premium when working out profit. Profit = payoff − premium.
- Mixing up call and put. Call gains when the price goes up; put gains when it goes down.
- Thinking margin is the price of the futures contract. Margin is only a safety deposit; you gain or lose on the full contract value.