Direct answer
A “worked example of rate hikes” is a fully specified numerical scenario that shows how an interest-rate increase can affect borrowing costs, expected cash flows, and—sometimes—foreign exchange (FX) through interest-rate expectations. The key is that the example is built from stated assumptions (for example, how markets form expectations and how quickly pricing changes). Because real markets vary, the worked example is a teaching tool, not a prediction.
What “rate hike” means (stable mechanics)
A rate hike is when a central bank raises one or more of its policy interest rates (or signals tighter policy). The stable mechanism is: higher policy rates generally make money more expensive in the economy, and they often change the expected path of future rates.
There are two common channels you can model:
- Domestic cash-flow channel: Higher rates increase discount rates or loan pricing, which can reduce the present value of future cash flows.
- Relative-rate and expectation channel for FX: FX prices often react to differences between expected interest rates and expectations about future policy, not only to the current level.
In an example, you must decide what is held constant (for instance, inflation, growth, credit risk, and market liquidity) and what is allowed to change (for instance, the discount rate and the expected future short rate).
Evidence or example: a fully assumed numerical scenario
Setup (all assumptions stated)
Assume:
- A central bank performs a single rate hike of +1.00% (from 2.00% to 3.00%).
- There are no other changes to credit risk, taxes, liquidity costs, or exchange-rate risk in the pricing model.
- A market participant prices a one-year claim that pays $100 at maturity.
- The participant uses a discount rate equal to the current policy rate (simplifying assumption).
Before the rate hike
- Discount rate: 2.00%
- Present value (PV): PV = 100 / (1 + 0.02) = 100 / 1.02 = $98.04 (rounded)
After the rate hike
- Discount rate: 3.00%
- PV: PV = 100 / (1 + 0.03) = 100 / 1.03 = $97.09 (rounded)
What changed in the model
- The PV falls by about $0.95 (98.04 − 97.09), reflecting that higher rates reduce the value of future payments.
Where the FX part would come from (still assumed)
To connect to FX without claiming a guaranteed result, you can extend the same logic:
- Assume the foreign currency appreciates relative to the domestic currency when domestic expected rates are higher than foreign expected rates.
- But you must also assume how quickly markets re-price expectations and whether other factors dominate (for example, risk sentiment, hedging flows, or surprise policy signals).
A second worked step could illustrate expectations rather than only the immediate level. For instance, assume markets expect that after the +1.00% hike, the policy rate will stay flat for the next year; then the discounting effect above is an approximate representation of that “expected path.” If instead markets expect further hikes or faster cuts, the effect would differ because the discount rate would not equal only the instant policy level.
Limitations and risks (material failure modes)
- Assumption mismatch: In real pricing, discount rates may reflect inflation expectations, credit risk, liquidity, and risk premia—not the policy rate alone.
- Expectation timing: Markets often react to the expected future path of policy. A worked example that assumes “only today changes” can diverge sharply.
- FX is multi-causal: FX moves can be driven by risk appetite, capital flows, terms of trade, and positioning. Rate hikes may be outweighed by these factors.
- Non-linear effects: Central bank communication, credibility, and market constraints can create jumps rather than smooth repricing.
Verification and next question
To independently verify concepts behind a worked example, focus on:
- Policy timeline: the announcement date and the effective date (what changed and when).
- Expectation proxy: how market rates or implied expectations moved around the announcement (rather than relying on the interest-rate change alone).
- Model check: whether the real-world pricing driver matches the example’s assumptions (for example, whether discounting actually tracks the policy rate).
Next question to ask yourself: In your scenario, what exactly is repriced—current rates, the expected path, or risk premia? The worked example is only as useful as that mapping.