Introduction to Derivatives

Level 0: Foundations | Module 0.2 | Time: 2 hours

🎯 Learning Objectives

By the end of this module, you will:

Understand what derivatives are and why they exist
Master call and put option mechanics
Read and interpret payoff diagrams
Learn essential options terminology
Grasp the fundamental use cases (hedging, speculation, income)

Prerequisites: Finance Fundamentals

What Are Derivatives?

A derivative is a financial contract whose value derives from an underlying asset.

Think of it as a contract about an asset, not ownership of the asset itself.

The Core Concept

Traditional Investment:
You buy 1 Bitcoin at $40,000 → You own the Bitcoin

Derivative:
You buy a contract that gives you the RIGHT (not obligation)
to buy 1 Bitcoin at $40,000 at some future date → You own a contract

Key Difference:

Owning Bitcoin: You have it now, price goes up/down, you gain/lose
Owning a derivative: You have a contract with specific terms and conditions

Why Derivatives Exist

1. Hedging (Insurance)

Protect against adverse price moves
Example: Airline buys oil derivatives to lock in fuel costs

2. Speculation (Bet on direction)

Leverage returns with less capital
Example: Trader thinks Bitcoin will rise, buys calls instead of Bitcoin

3. Income Generation

Earn premiums by selling derivatives
Example: Bitcoin holder sells call options for monthly income

4. Access

Gain exposure to assets you can’t or don’t want to own directly
Example: Bet on volatility itself, not just price direction

Options: The Building Blocks

An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an asset at a specified price before or at expiration.

Two Types of Options

1. Call Option

The right to BUY an asset at a specified price

Think: “I’m calling the asset to me”

Example:

You buy a Bitcoin Call Option with:
- Strike Price: $50,000
- Expiration: 30 days
- Premium Paid: $2,000

This gives you the RIGHT to buy 1 BTC at $50,000 anytime in the next 30 days.

Scenarios:

Scenario A: Bitcoin rises to $60,000

You exercise the call: Buy BTC at $50,000
Immediately worth $60,000
Profit: $60,000 - $50,000 - $2,000 (premium) = $8,000 ✅

Scenario B: Bitcoin falls to $35,000

You don’t exercise (why buy at $50k when market is $35k?)
Let option expire worthless
Loss: $2,000 (only the premium you paid) ❌

2. Put Option

The right to SELL an asset at a specified price

Think: “I’m putting the asset back to someone”

Example:

You buy a Bitcoin Put Option with:
- Strike Price: $40,000
- Expiration: 30 days
- Premium Paid: $1,500

This gives you the RIGHT to sell 1 BTC at $40,000 anytime in the next 30 days.

Scenarios:

Scenario A: Bitcoin falls to $30,000

You exercise the put: Sell BTC at $40,000 (above market)
Would only fetch $30,000 in market
Profit: $40,000 - $30,000 - $1,500 (premium) = $8,500 ✅

Scenario B: Bitcoin rises to $50,000

You don’t exercise (why sell at $40k when market is $50k?)
Let option expire worthless
Loss: $1,500 (only the premium you paid) ❌

Essential Terminology

Before we go further, let’s define the key terms you’ll see everywhere:

Underlying Asset

The asset the option contract is based on (Bitcoin, Ethereum, AAPL stock, etc.)

Strike Price (K)

The price at which you can buy (call) or sell (put) the underlying asset.

Example: “A $50,000 strike call” means you can buy at $50,000

Premium

The price you pay to buy the option. This is your maximum loss.

Think of it like an insurance premium - you pay upfront for protection/opportunity.

Expiration Date

When the option contract ends. After this, the option is worthless.

Common periods: 1 week, 30 days, 90 days, 1 year

Intrinsic Value

The value if you exercised the option right now.

For Calls: max(Spot Price - Strike Price, 0) For Puts: max(Strike Price - Spot Price, 0)

Example:

Bitcoin spot price: $45,000
Call with $40,000 strike: Intrinsic value = $5,000
Call with $50,000 strike: Intrinsic value = $0 (out of the money)

Put with $50,000 strike: Intrinsic value = $5,000
Put with $40,000 strike: Intrinsic value = $0 (out of the money)

Extrinsic Value (Time Value)

The extra premium beyond intrinsic value, representing the time left and volatility.

Premium = Intrinsic Value + Extrinsic Value

Example:

Bitcoin at $45,000
$40,000 strike call trading at $7,000

Intrinsic Value: $45,000 - $40,000 = $5,000
Extrinsic Value: $7,000 - $5,000 = $2,000

That $2,000 represents hope that Bitcoin will rise further before expiration.

In the Money (ITM)

Option has intrinsic value if exercised now.

Call ITM: Spot Price > Strike Price
Put ITM: Strike Price > Spot Price

At the Money (ATM)

Strike price ≈ Spot price (approximately equal)

Out of the Money (OTM)

Option has no intrinsic value if exercised now.

Call OTM: Spot Price < Strike Price
Put OTM: Strike Price < Spot Price

Quick Reference:

Bitcoin Spot: $45,000

Calls:
- $40,000 strike → ITM (in the money)
- $45,000 strike → ATM (at the money)
- $50,000 strike → OTM (out of the money)

Puts:
- $50,000 strike → ITM (in the money)
- $45,000 strike → ATM (at the money)
- $40,000 strike → OTM (out of the money)

Payoff Diagrams: Visual Options

Payoff diagrams show profit/loss at expiration based on the underlying asset’s price.

This is the single most important visual tool in options trading.

Long Call Payoff Diagram

Buying a Call Option

Profit/Loss
     ↑
     |                      ╱
     |                    ╱
     |                  ╱
     |                ╱
  ---|---------------
     |             ╱ Strike Price
     |           ╱
     |         ╱
     |-------╱  ← Max Loss = Premium Paid
     |________________→ Spot Price at Expiration

Key Features:

Max Loss: Premium paid (limited)
Max Gain: Unlimited (as price rises)
Break-even: Strike Price + Premium
Profit Zone: Above break-even (green)
Loss Zone: Below break-even (red)

Example Numbers:

Bought $50,000 strike call for $2,000 premium

Spot at Expiration | Intrinsic Value | Premium Paid | Profit/Loss
-------------------|-----------------|--------------|------------
$40,000            | $0              | $2,000       | -$2,000
$45,000            | $0              | $2,000       | -$2,000
$50,000 (strike)   | $0              | $2,000       | -$2,000
$52,000 (BE)       | $2,000          | $2,000       | $0
$55,000            | $5,000          | $2,000       | +$3,000
$60,000            | $10,000         | $2,000       | +$8,000
$70,000            | $20,000         | $2,000       | +$18,000

Long Put Payoff Diagram

Buying a Put Option

Profit/Loss
     ↑
     |    ╲
     |     ╲
     |      ╲
     |       ╲
  ---|--------╲------
     |         ╲  Strike Price
     |          ╲
     |           ╲
     |            ╲______  ← Max Loss = Premium Paid
     |____________________→ Spot Price at Expiration

Key Features:

Max Loss: Premium paid (limited)
Max Gain: Strike Price - Premium (large but limited)
Break-even: Strike Price - Premium
Profit Zone: Below break-even (green)
Loss Zone: Above break-even (red)

Example Numbers:

Bought $50,000 strike put for $1,500 premium

Spot at Expiration | Intrinsic Value | Premium Paid | Profit/Loss
-------------------|-----------------|--------------|------------
$60,000            | $0              | $1,500       | -$1,500
$55,000            | $0              | $1,500       | -$1,500
$50,000 (strike)   | $0              | $1,500       | -$1,500
$48,500 (BE)       | $1,500          | $1,500       | $0
$45,000            | $5,000          | $1,500       | +$3,500
$40,000            | $10,000         | $1,500       | +$8,500
$30,000            | $20,000         | $1,500       | +$18,500

Buying vs Selling Options

So far we’ve discussed buying options. But someone must sell them!

Selling (Writing) Options

When you sell an option, you:

Collect the premium upfront
Take on the obligation if the buyer exercises
Have limited upside (the premium) but potentially unlimited downside

This is the foundation of many structured products!

Short Call (Selling a Call)

You collect premium now, but must sell the asset at the strike if called

Payoff Diagram:

Profit/Loss
     ↑
     |________  ← Max Profit = Premium Collected
     |        ╲
     |         ╲  Strike Price
  ---|----------╲------
     |           ╲
     |            ╲
     |             ╲
     |              ╲ ← Unlimited Loss
     |_______________╲___→ Spot Price

Example:

You own 1 BTC (at $45,000)
You sell a $50,000 strike call for $2,000 premium

Scenario A: BTC at $48,000 at expiration
- Buyer doesn't exercise (below $50k strike)
- You keep premium: +$2,000
- You keep your BTC worth $48,000
- Total position value: $48,000 + $2,000 = $50,000

Scenario B: BTC at $60,000 at expiration
- Buyer exercises (above $50k strike)
- You must sell BTC at $50,000
- You keep premium: +$2,000
- Total: $50,000 + $2,000 = $52,000
- But you missed out on $60,000 - $52,000 = $8,000 upside

Short Put (Selling a Put)

You collect premium now, but must buy the asset at the strike if put to you

Payoff Diagram:

Profit/Loss
     ↑
     |             ________  ← Max Profit = Premium
     |           ╱
     |          ╱  Strike
  ---|--------╱-------
     |       ╱
     |      ╱
     |     ╱ ← Large Loss Potential
     |____╱________________→ Spot Price

Why Derivatives Matter for Structured Products

Structured products are built by combining derivatives!

Think of options as LEGO blocks:

Each piece (call, put, different strikes) has specific properties
Combine them creatively → create custom payoff profiles
Match any investor’s specific risk/return objectives

Examples We’ll Build:

Covered Call = Own BTC + Sell Call

Generates income from premiums
Caps upside but reduces cost basis

Principal Protected Note = Bond + Call Options

Protects your capital (bond)
Participates in upside (calls)

Range Accrual = Multiple short puts and calls

Earns yield if price stays in range
High income if volatility is low

The Three Primary Use Cases

1. Hedging (Insurance)

Real-World Analogy: Home insurance

You pay a small premium to protect against a large loss (house burns down).

Options Version: Put options as portfolio insurance

You own $100,000 of Bitcoin at $50,000
Worried about crash

You buy put options:
- Strike: $45,000 (10% below current)
- Cost: $2,000
- Expiration: 30 days

Result:
- If BTC crashes to $30,000 → Put protects you, exercise at $45,000
- If BTC rises to $60,000 → Put expires, but you made money on BTC
- Cost of insurance: $2,000 (2% of portfolio)

Why Hedge?

Peace of mind
Protect profits
Required for institutional risk management
Sleep better during volatile markets

2. Speculation (Leveraged Bets)

Leverage: Control large positions with small capital

Example: Bullish on Bitcoin

Option A: Buy Bitcoin Directly

Investment: $50,000
Buy: 1 BTC at $50,000

BTC rises to $60,000:
Profit: $10,000 (20% return)

BTC falls to $40,000:
Loss: $10,000 (20% loss)

Option B: Buy Call Options

Investment: $5,000 (buy 5 calls at $1,000 each)
Calls: $50,000 strike, 30 days

BTC rises to $60,000:
Each call worth: $10,000
Total: 5 × $10,000 = $50,000
Profit: $50,000 - $5,000 = $45,000 (900% return! 🚀)

BTC falls to $40,000:
Calls expire worthless
Loss: $5,000 (100% of investment, but less $ than owning BTC)

The Trade-off:

Massive leverage on upside (10x in this example)
Defined risk (can only lose $5,000, not $10,000)
Time decay (if BTC stays at $50k, options expire worthless)

Warning: This is speculative and risky! Most options expire worthless.

3. Income Generation

Selling options to collect premiums

This is the basis of many popular strategies:

Example: Covered Call Strategy

You own 1 BTC at $45,000
You sell a call option:
- Strike: $50,000
- Premium: $2,000
- Expiration: 30 days

Repeat monthly:
- Collect $2,000/month = ~4.4% monthly yield
- If BTC stays below $50k → keep BTC + premium
- If BTC goes above $50k → sell at $50k (still a profit)

Annual income: $2,000 × 12 = $24,000 (53% yield!)

Reality Check:

Premiums vary with volatility
You cap your upside
Works best in sideways/slightly bullish markets
Very popular strategy for income seekers

Option Pricing Fundamentals

What determines an option’s premium?

Five Key Factors

1. Spot Price vs Strike Price (Moneyness)

ITM options worth more (have intrinsic value)
OTM options worth less (only time value)

2. Time to Expiration

More time = higher premium
Time decay accelerates as expiration approaches

3. Volatility

Higher volatility = higher premium
More uncertainty = more valuable insurance

4. Interest Rates (Minor factor for short-term)

Higher rates = slightly higher call premiums

5. Dividends / Yield (For stocks/staking assets)

Higher dividends = lower call premiums

Quick Intuition

Why does volatility increase option value?

Scenario A: Bitcoin volatility is 20%
- Expected range in 30 days: $40k - $50k
- $55k call option unlikely to finish ITM
- Premium: $500

Scenario B: Bitcoin volatility is 80%
- Expected range in 30 days: $30k - $65k
- $55k call option has real chance to finish ITM
- Premium: $3,000

Higher volatility = wider range of outcomes = more value

Common Misconceptions

Myth 1: “Options are just gambling” Reality: Options are tools. Like a hammer can build or destroy, options can hedge or speculate. It’s about how you use them.

Myth 2: “Selling options is free money” Reality: You’re taking on risk. Collecting $2,000 premium is great until you have to buy BTC at $50k when it’s trading at $30k.

Myth 3: “Options are too complicated” Reality: Basic calls and puts are simple. Advanced strategies take time, but you can start with basics.

Myth 4: “I’ll get rich quick with options” Reality: Most retail options traders lose money. Respect the learning curve and risk.

Myth 5: “You have to exercise options” Reality: Most options are closed before expiration or expire worthless. Exercise is rare.

Practice Exercises

Exercise 1: Call Option Profit

Question: You buy a $45,000 strike call for $1,800. Bitcoin is at $52,000 at expiration. What’s your profit?

Click for solution

Intrinsic Value at Expiration:
$52,000 (spot) - $45,000 (strike) = $7,000

Profit/Loss:
$7,000 (intrinsic) - $1,800 (premium paid) = $5,200 profit ✅

Answer: $5,200 profit (289% return on $1,800 invested)

Exercise 2: Put Option Loss

Question: You buy a $50,000 strike put for $2,500. Bitcoin is at $55,000 at expiration. What’s your loss?

Click for solution

Intrinsic Value at Expiration:
$0 (put is OTM, spot > strike)

Profit/Loss:
$0 (intrinsic) - $2,500 (premium paid) = -$2,500 loss ❌

Answer: -$2,500 loss (100% of premium paid)

Lesson: Put was insurance against downside. Market went up, insurance not needed.

Exercise 3: Break-Even Calculation

Question: You buy a $48,000 strike call for $3,200. What spot price at expiration gives you break-even?

Click for solution

Break-Even Formula:
Break-even = Strike + Premium (for calls)

Break-even = $48,000 + $3,200 = $51,200

Answer: Bitcoin must be at $51,200 at expiration to break even.

Below $51,200 → Loss
Above $51,200 → Profit

Key Takeaways

1. Derivatives are contracts whose value derives from underlying assets

Not ownership, but rights and obligations
Building blocks for structured products

2. Calls give the right to buy, puts give the right to sell

Buyer has rights, seller has obligations
Premium is buyer’s max loss, seller’s max profit

3. Payoff diagrams visualize profit/loss scenarios

Essential tool for understanding any strategy
We’ll use these throughout the course

4. Options serve three purposes: hedging, speculation, income

Choose based on your goals and risk tolerance
Different strategies for different objectives

5. Five factors determine option prices

Spot vs strike, time, volatility, rates, dividends
Volatility is often the most important

What’s Next?

You now understand derivatives fundamentals! You’ve learned:

✅ What derivatives are and why they exist
✅ Call and put mechanics
✅ Payoff diagram interpretation
✅ Essential terminology
✅ Three primary use cases

You’re ready for structured products!

Continue to: What Are Structured Products →

This is where we combine these building blocks into sophisticated instruments.

Interactive Tools

Try It Yourself:

Option Payoff Diagram Builder - Visualize any option strategy
Option Pricer - See how factors affect premium
Structure Tool - Build your first covered call

Additional Resources

Videos (Recommended):

Khan Academy: Options Basics
Tastytrade: Options 101

Books:

“Options as a Strategic Investment” by Lawrence McMillan
“The Options Playbook” by Brian Overby

Practice:

Paper trade options before using real money
Use the FORGE tools to explore payoffs risk-free

Next Module: What Are Structured Products →

Or Continue Learning:

The Greeks - Advanced: How options change with market moves
Case Studies - Real-world option examples