## **Learning Outcomes**

After reading this article, you will be able to identify and explain the basic structure and features of options, including their potential payoffs for buyers and sellers. You will distinguish between inherent value and time value, and interpret how the main option price sensitivities (‘Greeks’: delta, gamma, theta) influence risk and strategy. You will be able to apply these principles to standard ACCA-style scenarios and calculations.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand the pricing, valuation, and risk characteristics of options. Focus your revision on the following syllabus areas relevant to this topic:

- The principles that underpin option contracts and their payoffs
- Recognition and calculation of option inherent value and time value
- Interpretation of the key 'Greek' sensitivities in option pricing (delta, gamma, theta)
- Application of option pricing theory (without requiring Black-Scholes calculations by hand)
- Importance of option sensitivities for risk management

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which party faces unlimited risk when selling a naked call option?
2. What is meant by the ‘inherent value’ of an option?
3. Delta measures the sensitivity of an option’s price to changes in:  
   a) Interest rates  
   b) Volatility  
   c) The reference asset price  
   d) Time to expiry
4. Briefly explain how time value affects an out-of-the-money option’s price.

## **Introduction**

Options play a central role in advanced financial management, providing flexible ways to manage or transfer risk. An option gives its holder the right – but not the obligation – to buy or sell a reference asset at a set price within a specified period. This article covers the key exam-relevant principles: the difference between inherent value and time value; how payoffs work for buyers and sellers; and how the main ‘Greeks’ (delta, gamma, theta) quantify risk exposure. Understanding these features is essential for tackling both calculations and narrative requirements on options in the ACCA AFM exam.

> **Key Term: option**  
> A contract granting the right, but not the obligation, to buy (call) or sell (put) an asset at a specified price (the exercise price), within a defined period.
>
> **Key Term: call option**  
> The right, but not the obligation, to buy the reference asset at the exercise price before expiry.
>
> **Key Term: put option**  
> The right, but not the obligation, to sell the reference asset at the exercise price before expiry.

## **OPTIONS: PAYOFF STRUCTURE**

Options present different risk and reward profiles for buyers and for sellers.

### Call and Put Options

- **Call option holder:** Gains if the reference asset rises above the exercise price. Maximum loss is limited to the premium paid.
- **Call option writer:** Gains only the premium received; faces potential losses if asset price rises significantly.

- **Put option holder:** Gains if the reference asset falls below the exercise price. Maximum loss is limited to the premium paid.
- **Put option writer:** Gains only the premium received; faces potential losses if asset price drops significantly.

### **Worked Example 1.1**

A European call option on a share has an exercise price of £10. The current share price is £9. The option premium is £0.50.

Calculate the payoff for the call option holder and writer at expiry if the share price ends at (a) £8, (b) £11.

> **Answer:**  
> (a) At £8: Option not exercised. Holder loses £0.50 premium; writer keeps £0.50.  
> (b) At £11: Holder exercises; profit = (£11 − £10) − £0.50 = £0.50. Writer’s loss = −£0.50 (payout) + £0.50 (premium) = £0.

## **INHERENT VALUE AND TIME VALUE**

Option prices consist of two main components, which you must be able to identify and distinguish in calculations and exam discussion.

> **Key Term: inherent value**  
> The amount by which an option is ‘in the money’: for a call, current asset price minus exercise price, or zero if negative; for a put, exercise price minus current asset price, or zero if negative.
>
> **Key Term: time value**  
> The excess of an option’s market price over its inherent value. Reflects expectations of future price movements, time to expiry, and volatility.

Option Value = Inherent Value + Time Value

- At expiry, time value is zero.
- Options with time left to expiry usually trade above their inherent value due to uncertainty.

### **Worked Example 1.2**

A share trades at £24. A three-month European put option with an exercise price of £25 is quoted at £1.10.

What are its inherent value and time value?

> **Answer:**  
> Inherent value = £25 − £24 = £1.  
> Time value = £1.10 − £1 = £0.10.

### **Revision Tip**

When answering questions on option value, always show the calculation of both inherent and time values separately.

## **OPTION PRICE SENSITIVITIES: THE GREEKS**

The ‘Greeks’ are measures used to assess how option prices respond to changes in market factors. Only delta, gamma, and theta are directly examinable in AFM.

> **Key Term: delta**  
> The sensitivity of an option’s price to changes in the price of the reference asset; mathematically, the expected change in option value for a £1 change in the reference.
>
> **Key Term: gamma**  
> The rate at which delta itself changes as the price of the reference changes.
>
> **Key Term: theta**  
> The rate at which an option’s price declines with the passage of time, all else held constant.

### Delta

- For calls, delta is positive (between 0 and 1). For puts, negative (between 0 and −1).
- High-delta options behave more like the reference asset.

### Gamma

- High gamma shows delta can change rapidly with even small moves in price.
- Important for dynamic hedging: when gamma is high, hedges must be frequently adjusted.

### Theta

- Options lose value as expiry approaches, assuming other factors remain unchanged.
- Theta is usually negative for option buyers (reflecting time decay).

### **Worked Example 1.3**

A portfolio manager sells 500 European call options with a delta of 0.6 per option. How many shares should the manager buy or sell to create a delta-neutral (hedged) position?

> **Answer:**  
> As the calls are sold, delta is −0.6 × 500 = −300. To offset, the manager should buy 300 shares.

### **Exam Warning**

Do not confuse gamma with delta: delta measures sensitivity to the reference asset price now; gamma measures how much that sensitivity could change.

## **Summary**

Options provide asymmetric payoffs, with risk limited for buyers and potentially unlimited for writers. Option premiums consist of inherent value (reflecting current profitability) and time value (reflecting the opportunity for gains before expiry). The Greeks (delta, gamma, theta) quantify price sensitivities and are critical for risk management, hedging, and interpreting option value changes in exam scenarios.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the basic payoff structure of calls and puts for buyers and sellers
- Distinguish between inherent value and time value in option pricing
- Recognise and interpret the key Greeks: delta, gamma, and theta
- Apply payoff and value calculations to standard option scenarios
- Understand how option sensitivities affect hedging and risk management strategies

## **Key Terms and Concepts**

- option
- call option
- put option
- inherent value
- time value
- delta
- gamma
- theta

Derivative instruments and pricing basics - Options: payoffs, Greeks, and inherent versus time value