Stock Options Explained

A beginner's interactive guide to understanding options — from the basics to hedging with delta

HKSI Paper 8 Curriculum

1. What is a Stock Option?

A right — but not an obligation — to buy or sell shares at an agreed price

Analogy: Imagine a voucher from a shop that says "You can buy this handbag for $500 any time in the next 3 months." You paid $30 for the voucher. If the handbag rises to $700, you use the voucher (profit $170). If the price drops to $400, you tear up the voucher and lose only the $30 you paid. That voucher is exactly like an option.

The Contract

A stock option is a contract between two parties:

Buyer (Holder)
Pays the premium
Gets the RIGHT
No obligation
Seller (Writer)
Receives the premium
Has the OBLIGATION
Must perform if exercised

The buyer decides whether to exercise. The seller must comply.

American vs European Style

American Style
Can be exercised at any time before or on the expiry date.
HK exchange-traded options are American style
European Style
Can only be exercised on the expiry date itself.
Common in index options

Key Terms

Underlying Asset
The stock (or index) the option is written on. E.g., HSBC shares.
Strike Price (K)
The fixed price at which you can buy/sell the underlying.
Premium
The price paid by the buyer to obtain the option. Non-refundable.
Maturity / Expiry
The last date the option can be exercised.
Exercise
Using the right granted by the option to buy or sell at the strike price.
Lot Size
One contract typically covers a fixed number of shares (e.g., 200 shares/contract in HK).

2. Call Options — The Right to BUY

A call gives you the right to purchase the underlying asset at the strike price

Call Option Payoff Calculator

EXERCISE
Spot $25 > Strike $20 — buy at $20, worth $25
Intrinsic Value
$5.00
max(0, S − K)
P&L for Long Call
+$2.00
Intrinsic − Premium

✓ Quick Check Examples — XYZ Stock, Strike $20

EXERCISE Spot = $25: Intrinsic = $25 − $20 = $5. Buy at $20, immediately worth $25. Profit $5 (minus premium).
DON'T Spot = $18: Intrinsic = max(0, $18 − $20) = $0. Cheaper to buy in the open market. Option is worthless. Loss = premium only.

Payoff Diagrams

Long Call — Max Loss: Premium | Breakeven: Strike + Premium | Upside: Unlimited

Long Call

BE: $23
Breakeven = Strike + Premium
Max Loss = Premium paid
Max Gain = Unlimited
When to use: You expect the stock to rise significantly. You pay a small premium for leveraged upside exposure with limited downside.

P&L formula: max(0, S − K) − Premium

3. Put Options — The Right to SELL

A put gives you the right to sell the underlying asset at the strike price

Put Option Payoff Calculator

EXERCISE
Spot $7 < Strike $10 — sell at $10, only worth $7 in market
Intrinsic Value
$3.00
max(0, K − S)
P&L for Long Put
+$1.00
Intrinsic − Premium

✓ Quick Check Examples — QST Stock, Strike $10

EXERCISE Spot = $7: Intrinsic = $10 − $7 = $3. Sell at $10 via option instead of market price $7. Profit $3 (minus premium).
DON'T Spot = $12: Intrinsic = max(0, $10 − $12) = $0. Better to sell at $12 in the open market. Option expires worthless. Loss = premium only.

Payoff Diagrams

Long Put — Max Loss: Premium | Breakeven: Strike − Premium | Max Profit: Strike − Premium

Long Put

BE: $8
Breakeven = Strike − Premium
Max Loss = Premium paid
Max Gain = Strike − Premium
When to use: You expect the stock to fall. Good for portfolio protection or speculating on a decline with limited downside.

P&L formula: max(0, K − S) − Premium

4. Option Premium = Intrinsic Value + Time Value

The price you pay has two components — what it's worth now, and the hope of more

Premium Decomposition Calculator

Intrinsic Value $5.00 Time Value $1.50
IV
TV
Intrinsic Value
$5.00
max(0, S−K)
Time Value
$1.50
Premium − IV
Total Premium
$6.50
IV + TV

✓ Quick Check 3 — Call Option, Strike $20, Premium $6.50

Spot $25 Intrinsic = $25 − $20 = $5.00. Time value = $6.50 − $5.00 = $1.50
Spot $18 Intrinsic = max(0, $18 − $20) = $0. Time value = $6.50 − $0 = $6.50 (all time value!)

✓ Quick Check 5 — Put Option, Strike $10, Time Value $1.50, Spot $7

PUT Intrinsic = $10 − $7 = $3.00. Premium = Intrinsic + Time Value = $3.00 + $1.50 = $4.50

Why Does Time Value Exist?

Time value represents the possibility that the option could move in your favour before expiry. The more time remaining, the greater the chance the stock moves. Time value decays to zero at expiry — this is called "theta decay."

Deep ITM Option
Mostly intrinsic value — acts like owning the stock. Time value is small.
ATM Option
Maximum time value — could go either way. Intrinsic = 0.
Deep OTM Option
Only time value remains. Small premium — it's a long shot.

5. Moneyness: ITM, ATM, OTM

Where the spot price is relative to the strike determines the option's "moneyness"

Interactive Moneyness Explorer

CALL OPTION
IN THE MONEY
|
PUT OPTION
OUT OF THE MONEY

Moneyness Reference Table

State Abbreviation Call Option Put Option Intrinsic Value
In The Money ITM Spot > Strike Spot < Strike Positive (intrinsic > 0)
At The Money ATM Spot = Strike Spot = Strike Zero (intrinsic = 0)
Out of The Money OTM Spot < Strike Spot > Strike Zero (worthless if exercised)

6. The Option Writer (Seller)

Writers collect premium upfront but carry the obligation — the mirror image of the buyer

Call Writer

Receives premium. Obligated to SELL shares at the strike price if the buyer exercises.

Market view: Bearish or neutral — expects the stock to stay below the strike price.

Put Writer

Receives premium. Obligated to BUY shares at the strike price if the buyer exercises.

Market view: Bullish or neutral — expects the stock to stay above the strike price.

Rights & Obligations — All Four Positions

Position Action Right or Obligation? Premium Market View Max Profit Max Loss
Long Call BUY the underlying RIGHT Pays Bullish Unlimited Premium
Short Call SELL the underlying OBLIGATION Receives Bearish/Neutral Premium Unlimited
Long Put SELL the underlying RIGHT Pays Bearish K − Premium Premium
Short Put BUY the underlying OBLIGATION Receives Bullish/Neutral Premium K − Premium

7. Factors Affecting Option Prices

Six key inputs that drive the option premium — drag each slider to see the impact

FACTOR
ADJUST
CALL
PUT

Key Insight: Volatility

Volatility is the only factor that increases BOTH call and put prices. Higher volatility = larger potential swings = more chance the option expires profitable. This is why option sellers demand higher premiums when markets are volatile.

Remember: Dividends reduce the stock price on the ex-dividend date. This benefits put holders (stock falls) and hurts call holders.

8. Delta (Δ) — The Hedge Ratio

Delta measures how much an option price changes when the stock price moves by $1

What is Delta?

Delta = Change in Option Price ÷ Change in Stock Price

Long Call / Short Put
Delta between 0 and +1
As stock rises $1, option price rises by delta.
Long Put / Short Call
Delta between -1 and 0
As stock rises $1, option price falls by |delta|.

Delta vs Moneyness

MoneynessCall DeltaPut DeltaMeaning
Deep ITM≈ +1≈ −1Moves like the stock itself
ATM≈ +0.5≈ −0.550% chance of expiring ITM
Deep OTM≈ 0≈ 0Barely reacts to stock moves

Delta Hedging Calculator — Jose's Example

Jose holds shares and wants to hedge using put options. How many contracts does he need?

Shares held1,200
÷ (|Delta| × Lot size)(0.60 × 200) = 120
= Contracts needed10 contracts
If stock drops $1:
Stock Position Loss
−$1,200
1,200 shares × $1
Put Option Gain
+$1,200
10 × $0.60 × 200
Net P&L: $0 — Perfectly Hedged!

9. Key Takeaways

Everything you need to remember about stock options

Basics

  • An option is a right (not obligation) to buy/sell at the strike price
  • Buyer pays premium; seller (writer) receives premium
  • HK exchange-listed options are American style — exercise any time
  • Call = right to BUY; Put = right to SELL
  • Always exercise when intrinsic value > 0

Premium Formula

  • Premium = Intrinsic Value + Time Value
  • Call intrinsic = max(0, S − K)
  • Put intrinsic = max(0, K − S)
  • Time value decays to zero at expiry
  • ATM options have maximum time value

Moneyness

  • ITM call: S > K | ITM put: S < K
  • ATM: S = K (for both)
  • OTM call: S < K | OTM put: S > K
  • Only ITM options have intrinsic value
  • ATM ≈ delta 0.5; ITM ≈ delta 1; OTM ≈ delta 0

Payoff Breakevens

  • Call breakeven = Strike + Premium
  • Put breakeven = Strike − Premium
  • Long call: unlimited upside, max loss = premium
  • Short call: max profit = premium, unlimited loss
  • Delta hedge: contracts = shares ÷ (|Δ| × lot size)

6 Factors Affecting Price

Spot ↑ → Call ↑, Put ↓
Strike ↑ → Call ↓, Put ↑
Interest rate ↑ → Call ↑, Put ↓
Volatility ↑ → Call ↑, Put ↑
Time to expiry ↑ → Call ↑, Put ↑
Dividend ↑ → Call ↓, Put ↑
Good luck on HKSI Paper 8!
Interactive Explainer — All concepts from HKSI Paper 8 curriculum