Understanding Options: A Practical Introduction to Derivatives and Strategic Positioning

A generic boilerplate foreign exchange option agreement

An introduction to options

What is an option? At its core, an option is a financial contract that grants the holder the right - but not the obligation - to require the counterparty to either buy or sell a specified asset at a predetermined price. Options come in two primary forms: call and put. A call option gives the holder the right to buy the underlying asset at the agreed strike price, while a put option gives the holder the right to sell the asset at that same price.

Viewed from the counterparty’s perspective, the call option represents a potential future obligation to sell the asset, and the put option a potential obligation to purchase it - should the holder choose to exercise the right. Importantly, this asymmetry is what distinguishes options from other derivative instruments such as forwards and futures, where both parties are obligated to transact at maturity regardless of how the market has moved.

Options may also be classified by their structure. An American option is exercisable at any point between its initiation and maturity. A European option, by contrast, may only be exercised on the expiration date itself. There are also Asian options, whose payoff depends on the average price of the underlying asset over a predetermined period. These are often used in contexts where reduced sensitivity to short-term price swings is desirable, but they will not be discussed further here. American options are the dominant form in U.S. stock and ETF markets, including those on companies such as Apple or Tesla. European options are more commonly used in index derivatives, such as those on the FTSE 100 or S&P 500, as well as in options on futures contracts.

The optionality embedded in these contracts comes at a cost. Because the holder is not required to exercise the contract, options must be purchased, typically through the payment of an upfront premium. This contrasts with forwards and futures, which do not involve such a cost to initiate (although margin requirements may apply, as discussed elsewhere).

In practice, the value of an option varies according to several factors, including the relationship between the strike price and the current price of the underlying asset, and the time remaining until expiration. For call options, as the strike price increases, the option becomes less likely to finish in the money - that is, less likely to be profitable by expiry - which in turn reduces both its immediate intrinsic value and the chance of a favourable outcome. Accordingly, higher-strike call options tend to have lower prices. For put options, the relationship is reversed: as the strike price increases, the potential payoff becomes larger and the likelihood of the option ending in the money increases, so the price of the put typically rises.

Time to maturity also plays a critical role. The longer the time until expiration, the greater the opportunity for favourable market movements, and hence the more valuable the option. Put differently, the longer the option remains alive, the longer the writer is exposed to market risk - uncertainty that the buyer may ultimately act on. This extended exposure contributes to the higher premium that longer-dated options tend to command.

Consider a trader who purchases a call option: they pay a premium in exchange for the right to buy the asset at a fixed price, potentially profiting if the market price rises above that level. By contrast, a trader who sells a put option receives a premium upfront but may incur significant losses if the asset's price falls below the strike. These scenarios illustrate the asymmetric risk and reward profiles that define options and underpin their flexibility as instruments for speculation, hedging, and strategic positioning in financial markets. We will move to consider all the above in some more detail.

Call options

Suppose an investor buys a European call option on 100 shares with a strike price of $100. At the time of purchase, the stock is trading at $98, the option expires in four months, and the premium is $5 per share - an outlay of $500 in total. Because this is a European-style contract, exercise is only possible at expiration.

If at maturity the stock price, S_T​, is below $100, the option expires worthless, and the investor’s loss is limited to the initial $500 premium paid. However, whenever S_T > $100, it becomes optimal to exercise. For example, if S_T =$115, exercising allows the purchase of 100 shares at $100 each. Immediately selling those shares at $115 generates $1,500 in proceeds, resulting in a gross gain of $1,500 – $1,000 = $500. After subtracting the $500 premium, the net profit is $1,000.

More generally, for each share the payoff at expiration is:

max (S_T − K, 0) where K=100,

and the net profit per share is:

max (S_T − K, 0) − 5.

It is worth noting that exercise can still be optimal even when it appears to yield a small gross gain. If S_T =$102, exercising produces a gross gain of $2 per share but, after accounting for the $5 premium, leaves a net loss of $3. Declining to exercise would forfeit the entire $5 premium, a worse outcome. In fact, for any S_T > K, exercising minimises losses or maximises gains, so European call holders always exercise at expiration if the option finishes in the money.

Put options

In contrast to a call buyer - who benefits from rising prices - a put option buyer profits when the underlying asset falls below the strike price. Let’s examine a concrete case.

Suppose an investor purchases a European put option with a strike price of $70, giving the right (but not the obligation) to sell 100 shares at that price. The stock is currently trading at $65, the option expires in three months, and the premium is $7 per share - amounting to a total initial investment of $700.

As this is a European option, it can only be exercised at expiration. If the stock price at that time, S_T, ​is above $70, the put finishes out-of-the-money and expires worthless. The investor incurs a total loss of $700 - the premium paid. But if S_T < 70, the option is exercised. For instance, if S_T = $55, the investor can buy 100 shares at $55 and sell them for $70 under the option terms. That’s a gain of $15 per share, or $1,500 total. After subtracting the original $700 premium, the net profit is $800.

The profit from holding one put option (on one share) at expiry is given by:

Max (K − S_T, 0) – 7   where K = 70.

Just as with call options, the decision at expiry is straightforward: if the option finishes in the money (i.e., S_T < K), it should always be exercised. Even if the net result is a loss, exercising minimises the loss compared to letting the option lapse entirely.

Option Positions: Longs, Shorts, and Payoff Symmetry

Every option contract has two sides: a long position, taken by the investor who buys the option, and a short position, taken by the investor who sells - or writes - the option. The buyer pays a premium to acquire the right to exercise the option under predefined terms. The seller, in turn, receives this premium up front but assumes a potential liability depending on how the market evolves. The financial outcomes for these two parties are inversely related: the profit or loss of the option writer is effectively the mirror image of the buyer’s outcome.

To illustrate, consider the two examples discussed earlier. For the call option, the writer receives $5 per share when the contract is initiated. If the stock finishes below the $100 strike, the option expires worthless, and the writer retains the full premium as profit. However, as the final stock price rises above $100, losses begin to accrue. If the stock ends at $120, the option holder will exercise the right to buy at $100, forcing the writer to deliver shares at a $20 discount - leading to a net loss of $15 after accounting for the premium received. Similarly, in the case of the European put, the writer collects $7 per share. If the stock finishes above the $70 strike, the option expires unexercised, and the writer retains the premium. But if the stock drops to, say, $55, the writer must purchase shares at $70 from the option holder and immediately incur a $15 loss per share, resulting in a net loss of $8 after the premium is considered.

These outcomes reflect the four basic types of option positions: (1) a long call, which benefits from rising prices; (2) a long put, which benefits from falling prices; (3) a short call, which profits when prices remain below the strike; and (4) a short put, which profits when prices remain above the strike. The key difference lies in the asymmetry of risk and reward. For buyers, the maximum loss is limited to the premium paid, while the upside is potentially significant. For writers, the maximum gain is capped at the premium received, but the downside - particularly with uncovered call writing - can be substantial.

To focus solely on how options behave at expiration, it's common to define the payoff separately from the premium. If K denotes the strike price and S_T ​ the terminal price of the underlying asset, then the payoff from a long call is:

max (ST − K, 0),

since the holder only benefits if the asset ends above the strike. The payoff to a short call is the negative of that, or:

min (K − ST, 0).

For puts, the payoff to the long position is:

max (K − S_T, 0),

as the holder profits when the asset falls. The short put position again yields the inverse:

min (S_T − K, 0).

These formulas hopefully convey the essential financial logic of option contracts. However, all of the above positions are represented diagrammatically here:

European option payoffs

The reader will begin to see here that combinations of options can be used to engineer what are known as synthetic positions - portfolios that replicate the payoffs of other financial instruments. While we won’t explore these constructions in full here, consider a simple example: suppose a trader simultaneously takes a long position in a European call and a short position in a European put, both with the same strike price K and the same expiration date. What is the result?

A long call produces a positive payoff when the final asset price S_T ​ exceeds K, and nothing otherwise. A short put, meanwhile, results in a loss when S_T < K, and zero otherwise. When combined, these two options generate a net payoff of S_T – K at expiration - positive if the asset rises above the strike, negative if it falls below. This is precisely the payoff of a long forward contract with forward price K. Accordingly, this combination of options replicates a synthetic forward position. If the options are entered into at zero net premium, the equivalence is exact. This is clearly seen below:

Synthetic long forward, from similtaneous holding of a long call and short put

Underlying Assets

Options are not confined to individual shares - they are traded on a wide range of underlying assets, including exchange-traded products, currencies, stock indices, and futures contracts. While each asset class has its own trading conventions and contract specifications, the fundamental mechanics of options apply consistently across them.

In the UK and the US, most equity options are traded on exchanges such as the CBOE and NYSE Euronext. A standard stock option contract typically represents 100 shares, aligning with standard market trading units. In addition to individual equities, exchanges also offer options on exchange-traded products (ETPs), such as exchange-traded funds (ETFs), which are designed to track the performance of market indices, sectors, commodities, or currencies. For example, the SPDR S&P 500 ETF allows investors to gain exposure to the performance of the S&P 500 index.

Currency options are mainly traded over the counter (OTC), but some are available on exchanges, such as NASDAQ OMX. These exchange-traded currency options are usually European-style and cover 10,000 units of the underlying currency (or 1,000,000 in the case of the Japanese yen).

Index options - such as those based on the S&P 500, the Nasdaq-100, or the Dow Jones Industrial Average - are also widely traded. These contracts are typically cash-settled and European in style, meaning they can only be exercised at expiry. Rather than delivering the underlying shares, the payoff is settled in cash based on the difference between the strike price and the index level at expiry.

Futures options add yet another dimension. These are options written on futures contracts rather than the physical asset itself and are usually American style. If exercised, they result in a position in the underlying futures contract. Futures options typically expire shortly before the underlying futures themselves and are commonly used for hedging or directional trading in commodities and interest rate markets.

These diverse instruments demonstrate the flexibility of options as a framework for managing risk and expressing market views across asset classes.

Conclusion

This introduction has provided a foundational overview of options, beginning with their basic structure and extending to the range of underlying assets on which they are traded. We have examined how call and put options allow investors to express directional views, how the asymmetry between buyer and seller payoffs creates unique risk profiles, and how these instruments differ fundamentally from linear contracts such as forwards and futures.

Through illustrative examples, we have demonstrated how an option’s value is shaped by the relationship between the strike price and the market price at expiry. We also introduced the idea of combining options to construct synthetic positions - highlighting the flexibility and strategic potential of these instruments. Whether used for hedging, speculation, or portfolio design, options are among the most powerful and adaptable tools in modern financial markets.

It should be clear to more experienced readers that this treatment has been intentionally introductory. Topics such as trading costs, margin requirements, clearing mechanisms, regulatory frameworks, and taxation - particularly as they pertain to the over-the-counter (OTC) markets - are best explored in the context of financial legislation and infrastructure, which will be addressed in future articles.

For now, this primer is intended to bridge the gap for those looking to enter the world of finance without the time or means to pursue a full academic degree in economics. It provides the necessary foundation to begin engaging with the field thoughtfully, and prepares the reader for deeper study of options pricing, valuation models, and applied strategy in subsequent discussions.

Any queries, feel free to contact me via. LinkedIn at: www.linkedin.com/in/jameswbward1

Text used:

Hull, J.C. (2022) Options, futures, and other derivatives. 11th edn. Harlow: Pearson, pp. 31-33; pp. 227-233