Derivatives & Options: Types, Valuation, Payoffs & Strategies

TAKEAWAYS:

• Derivatives are contracts whose value depends on an underlying asset (e.g., stocks, commodities, indices), used for hedging, speculation, or arbitrage.
• Options (calls/puts) give the right (not obligation) to buy/sell at a strike price; their value = intrinsic value + time value.
• Futures vs. forwards: Futures are exchange-traded (standardized, marked-to-market), while forwards are OTC (customizable, settled at maturity).
• Payoff diagrams visually show profits/losses for buyers/sellers of options—critical for exam questions.
• Black-Scholes model (for European options) and binomial trees (for American options) are key valuation tools.
• Strategies like straddles, spreads, and hedging combine options to manage risk or bet on volatility.

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1. What Are Derivatives?

Derivatives are financial instruments whose value is derived from an underlying asset (e.g., stocks, commodities, currencies, or market indices). They allow investors to hedge risk, speculate, or lock in prices without owning the asset.

Types of Derivatives

Why Use Derivatives?

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2. Forwards vs. Futures: Key Differences

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3. Options: Calls and Puts

Options give the right (not obligation) to buy (call) or sell (put) an asset at a strike price by the expiration date, paying a premium.

Key Terms

• Strike Price (X): Agreed-upon price to buy/sell.
• Premium (P): Upfront cost of the option.
• Intrinsic Value: max(0, S - X) for calls; max(0, X - S) for puts (where S = spot price).
• Time Value: Premium – Intrinsic Value (erodes as expiration nears).

When to Exercise an Option?

• Call Option: Exercise if market price (S) > strike price (X). Example: You buy a call option on Delta Company (DC) stock at Rs. 350 (strike) for a Rs. 25 premium. If DC’s stock rises to Rs. 400, you exercise to buy at Rs. 350 and sell at Rs. 400, profiting Rs. 75 – Rs. 25 premium = Rs. 50 per share.
• Put Option: Exercise if market price (S) < strike price (X). Example: A put option on Ncell stock with strike Rs. 160 and premium Rs. 10. If Ncell falls to Rs. 140, you sell at Rs. 160, profiting Rs. 20 – Rs. 10 premium = Rs. 10 per share.

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4. Payoff Diagrams: Visualizing Option Profits

Worked Example: Call Option Payoff

• Given:
  • Call option premium = Rs. 25
  • Strike price (X) = Rs. 350
  • Market price (S) = Rs. 400
• Calculations:
  • Intrinsic Value = Rs. 400 – Rs. 350 = Rs. 50
  • Profit = Intrinsic Value – Premium = Rs. 50 – Rs. 25 = Rs. 25 per share
  • Seller’s Loss = Rs. 25 (premium) + (Rs. 400 – Rs. 350) = Rs. 75

Real-World Tie-In: Daraz’s dynamic pricing uses options-like logic to adjust prices in real-time based on demand (like a "call option" on inventory). If demand spikes (high "market price"), Daraz may "exercise" higher prices, similar to how a call option holder profits from rising stock prices.

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5. Option Valuation Models

A. Binomial Option Pricing Model (American Options)

Used for options that can be exercised anytime before expiration. Steps:

1. Build a price tree for the underlying asset.
2. Calculate option values at each node.
3. Work backward using risk-neutral valuation.

B. Black-Scholes Model (European Options)

For options exercisable only at expiration, the formula is: $$C=S_{0}N(d_1)-X{e}^{-rT}N(d_2)$$ $$d_1=\frac{\ln (S_0/X)+(r+{\sigma }^2/2)T}{\sigma \sqrt{T}},d_2=d_1-\sigma \sqrt{T}$$

• $C$ = Call option price
• $S_0$ = Current stock price
• $X$ = Strike price
• $r$ = Risk-free rate
• $\sigma$ = Volatility
• $T$ = Time to expiration

Example (Nepal Context): Valuing a call option on NEPSE’s NIFTY 50 index:

• $S_0=3,000$ points, $X=2,900$, $r=8\%$, $\sigma =20\%$, $T=0.5$ year.
• Plug into Black-Scholes to find $C$.

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6. Option Strategies

Combine calls/puts to create strategies for hedging or speculation.

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7. Swaps: Exchanging Cash Flows

Swaps are agreements to exchange cash flows (e.g., interest payments, currencies). Common types:

• Interest Rate Swap: Exchange fixed for floating rates (e.g., a company pays fixed, receives floating).
• Currency Swap: Exchange principal + interest in different currencies (e.g., NTC swaps USD for INR).

Real-World Example: Global banks use swaps to hedge interest rate risk. For example, a Nepali bank borrowing in USD might swap its floating-rate debt for fixed-rate payments to stabilize costs.

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8. Risks of Derivatives

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In the Real World

1. NEPSE Futures (Nepal):

   • Idea Used: Futures contracts on the NIFTY 50 index allow investors to hedge against market downturns or speculate on index movements.
   • How: For example, a fund manager might sell NIFTY 50 futures to lock in profits if they expect the index to fall, similar to short-selling but with leverage.

2. Khalti’s Dynamic Pricing (Nepal):

   • Idea Used: Options-like pricing logic adjusts transaction fees based on demand (e.g., higher fees during festival seasons = "exercising" higher prices like a call option).
   • How: If Khalti detects high transaction volumes (high "market price"), it may dynamically increase fees to manage load, akin to a call option’s premium adjusting to demand.

3. Daraz’s Inventory Management (Global):

   • Idea Used: Real options theory treats inventory as an option to fulfill future demand.
   • How: Daraz may hold less stock (like a "put option" on inventory) and order dynamically based on real-time demand signals, reducing holding costs.

4. Ncell’s Foreign Currency Hedging:

   • Idea Used: Currency swaps to hedge against USD/NPR exchange rate fluctuations.
   • How: Ncell might enter a swap to convert future USD revenues into NPR at a fixed rate, protecting against depreciation.

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Exam Tip

1. Memorize Payoff Formulas:

   • For calls: Profit = max(0, S – X) – Premium
   • For puts: Profit = max(0, X – S) – Premium
   • Exam questions often ask for payoffs at specific prices—practice these calculations!

2. Diagrams Are Key:

   • Draw payoff diagrams for calls/puts under different scenarios (e.g., at-the-money, in-the-money, out-of-the-money).
   • Label axes clearly: Profit/Loss (Y-axis) vs. Stock Price (X-axis).

3. Real-World Applications:

   • Link options to hedging (e.g., farmers, banks) or speculation (e.g., traders).
   • For swaps, explain how they’re used in interest rate risk management (e.g., banks, corporates).

4. Black-Scholes Shortcuts:

   • Know the Greeks (Delta, Gamma, Vega) are often tested—briefly explain their impact (e.g., Delta = sensitivity to price changes).
   • For numerical questions, show all steps (e.g., calculating $d_1$ and $d_2$).

5. Common Pitfalls:

   • Forwards vs. Futures: Don’t confuse OTC (forwards) with exchange-traded (futures).
   • American vs. European Options: American options can be exercised early; European cannot.
   • Premium vs. Intrinsic Value: Time value = Premium – Intrinsic Value (critical for valuation questions).

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Final Note: Derivatives are powerful tools but require careful analysis. Focus on payoff diagrams, valuation models, and real-world hedging examples—these will earn you full marks in exams!