Interest Rates & Derivatives: Swaps, Bonds & Yield Curves

TAKEAWAYS:

• Interest rates directly impact the pricing of derivatives like swaps, futures, and options, creating an inverse relationship between rates and call option values.
• Interest rate swaps allow entities to exchange floating for fixed rates, used by banks and NEPSE to hedge against rate volatility.
• Yield curves (normal, inverted, humped) reflect market expectations and are critical for pricing bond derivatives.
• Bond forwards and futures let investors lock in yields before maturity, reducing reinvestment risk.
• Collateralized debt obligations (CDOs) and mortgage-backed securities (MBS) derive value from interest rate movements, popular in global markets.
• Nepal’s NEPSE uses interest rate derivatives to manage portfolio risks in volatile economic conditions.

1. Interest Rates and Derivative Valuation

Interest rates are the foundation of derivative pricing. They determine the time value of money, affecting:

• Futures and forwards: Higher rates reduce forward prices (due to higher discounting).
• Options: Call options lose value as rates rise (inverse relationship), while puts gain value.
• Swaps: Fixed vs. floating rate exchanges are priced based on interest rate differentials.

Key Relationships

graph TD
    A["Interest Rate ↑"] --> B["Futures/Forwards Price ↓"]
    A --> C["Call Option Value ↓"]
    A --> D["Put Option Value ↑"]
    A --> E["Swap Fixed Rate ↑"]

Why?

• Futures/Forwards: Higher rates increase discounting, lowering forward prices.
• Calls: Higher rates reduce present value of exercise price, lowering call premiums.
• Puts: Higher rates increase the cost of holding the underlying, boosting put values.

2. Interest Rate Swaps

An interest rate swap is a derivative where two parties exchange cash flows based on different interest rate indices (e.g., floating vs. fixed).

How It Works

• Notional Principal: The fixed amount on which interest is calculated (e.g., Rs 100 million).
• Payment Dates: Typically semi-annual or annual.
• Reference Rates: LIBOR, SOFR, or Nepal’s Nepal Rastra Bank (NRB) benchmark rate.

Example: Nepal Bank vs. Global Bank Swap

sequenceDiagram
    participant BankA as Nepal Bank
    participant BankB as Global Bank
    BankA->>BankB: Pays floating (NRB rate + 0.5%)
    BankB->>BankA: Pays fixed 5.5% on Rs 50M

Why?

• Nepal Bank wants to lock in fixed costs (e.g., loan repayments).
• Global Bank wants to hedge against floating rate hikes.

3. Bond Derivatives and Yield Curves

(a) Bond Forwards and Futures

• Bond Futures: Standardized contracts (e.g., NEPSE’s Government Securities Futures) to hedge bond price risk.
• Bond Forwards: Custom contracts to lock in yields before maturity.

Worked Example: NEPSE Bond Forward

• Spot Yield: 6.5% (annual)
• Forward Rate: 7.2% (due to expected rate hike)
• Investor enters a forward to buy a Rs 10M bond at 6.5% yield, locking in lower cost.

(b) Yield Curve Analysis

The yield curve plots interest rates vs. maturities. Key shapes:

4. Collateralized Debt Obligations (CDOs) and MBS

• Mortgage-Backed Securities (MBS): Bundles of home loans (e.g., Nepal’s housing finance companies).
• CDOs: Layered securities backed by MBS/bonds (popular in global markets like Google’s early-stage investments).

How Interest Rates Affect MBS:

• Rate ↑ → Mortgage prepayments ↓ → MBS prices ↓.
• Rate ↓ → Prepayments ↑ → MBS prices ↑.

5. Real-World Applications in Nepal

(a) NEPSE’s Interest Rate Hedging

• Scenario: NEPSE portfolio managers use interest rate swaps to hedge against NRB rate changes.
• Tool: Nepal Rastra Bank’s benchmark rate swaps to lock in fixed costs.

(b) Banks’ Loan Risk Management

• Scenario: NMB Bank issues floating-rate loans but uses IR swaps to convert to fixed rates.
• Outcome: Stable loan repayments despite NRB rate fluctuations.

6. Exam Tip

• Focus on:
  • Interest rate vs. derivative value relationships (e.g., calls lose value when rates rise).
  • Swap mechanics (notional, payment dates, reference rates).
  • Yield curve shapes (normal/inverted/humped) and their implications.
• Common Pitfalls:
  • Misapplying continuous vs. simple compounding in option pricing.
  • Confusing floating vs. fixed legs in swaps.
• Worked Example Style:
  • Always show step-by-step calculations (e.g., forward price adjustment for storage costs).
  • Use Nepali business cases (e.g., Kathmandu’s Nepal Investment Bank).

Worked Example: Forward Contract on Silver (Adapted from Past Exam)

Given:

• Spot price = Rs 1,500/Tola
• Storage cost = Rs 50/Tola (paid semi-annually)
• Risk-free rate = 8% (annual, continuous compounding)
• Time to maturity = 1 year

Step 1: Calculate Cost of Carry The forward price adjusts for:

1. Storage cost: Rs 50 × 2 = Rs 100 (total for 1 year).
2. Interest: Rs 1,500 × e^(0.08×1) ≈ Rs 1,627.50.

Forward Price Formula: $$F=S\times e^{rT}+C$$ Where:

• $S$ = Spot price (Rs 1,500)
• $r$ = Risk-free rate (8%)
• $T$ = Time (1 year)
• $C$ = Storage cost (Rs 100)

$$F=1,500\times e^{0.08}+100\approx 1,627.50+100=\text{Rs 1,727.50/Tola}$$

Comparison Table: Swap Types

Advantages & Disadvantages of Interest Rate Derivatives

Exam Tip Recap

• Memorize: The inverse relationship between interest rates and call options.
• Calculate: Forward prices using cost-of-carry models.
• Apply: Swap mechanics to Nepal’s banking/NEPSE scenarios.
• Visualize: Always sketch yield curves and swap payment flows.