How Level II tests carry logic, no-arbitrage pricing, and value changes in equity, rate, and fixed-income forwards and futures.
Level II derivatives start with a blunt question: what price keeps arbitrage away? The exam is usually less interested in naming the contract than in whether you can identify the correct carry inputs, separate price from value, and see how the contract should react when rates, coupons, or dividends change.
Many candidates remember formulas but miss the setup:
Level II is usually testing that setup discipline first.
flowchart TD
A["Start with current spot"] --> B["Check known cash flows"]
B --> C["No income before expiry"]
B --> D["Income or coupon before expiry"]
C --> E["Carry spot at the financing rate"]
D --> F["Subtract PV of income then carry forward"]
E --> G["No arbitrage forward price"]
F --> G
G --> H["Compare to market contract price"]
H --> I["Mispricing implies arbitrage trade"]
That flow is more durable than memorizing a separate formula for every underlying.
For an asset with no cash flows, a simple discrete-time no-arbitrage forward price is:
$$ F_0(T)=S_0(1+r)^T $$
If the underlying pays known cash flows before expiration:
$$ F_0(T)=\bigl(S_0-\operatorname{PV}(I)\bigr)(1+r)^T $$
| Situation | Core pricing adjustment |
|---|---|
| Equity with no dividends | Grow current spot at the financing rate |
| Equity with known dividends | Subtract present value of dividends before carrying forward |
| Bond forward | Start from dirty price and subtract present value of coupons received before delivery |
| Short-term rate forward or futures | Use the implied financing-rate relationship for the future borrowing or lending period |
The exam often gives enough data to compute the correct carry adjustment, but hides it inside the vignette rather than presenting it as a clean bullet list.
At initiation, the contract price is set so the contract value is approximately zero. After market conditions move, the existing position gains or loses value.
For a long forward on a non-income-paying asset, a common value expression at time (t) is:
$$ V_t=S_t-\operatorname{PV}_t(F_0) $$
That is the part candidates often miss. The contracted delivery price is fixed, but the market forward price is not.
| Question type | What the exam is really testing |
|---|---|
| Calculate the no-arbitrage forward price | Whether you selected the right carry inputs |
| Calculate the value of an existing forward | Whether you understand that market conditions changed after initiation |
| Identify an arbitrage trade | Whether you can compare the quoted contract to the model price and trade the difference logically |
Level II usually wants the pricing intuition first:
The most useful exam instinct is to ask which source of carry matters most:
| Contract family | What usually drives the correct answer |
|---|---|
| Bond forward or bond future | Coupon timing, accrued interest, benchmark financing rate |
| FRA or rate forward | The implied future borrowing or lending rate for the reference period |
| Interest-rate future | The link between the quoted futures contract and the future short-rate exposure it represents |
The exam often inserts a coupon date or a settlement-timing detail because that is what separates a strong answer from a formula dump.
An equity index forward expires in six months. The vignette gives the spot index level, the financing rate, and a scheduled cash dividend from the underlying basket.
A weak answer compounds the full spot level and ignores the dividend.
A stronger answer recognizes that the dividend reduces the net carry base before the financing step, which lowers the correct no-arbitrage forward price.
Which input most directly lowers the no-arbitrage forward price of an equity index contract, all else equal?
Best answer: A higher present value of dividends paid before expiration.
Why: Those dividends are benefits to holding the underlying, so they reduce the carried net spot amount that supports the forward price.