Derivatives

• Topic 01

  Derivatives Valuation Framework

  24 questions
• Topic 02

  Forward and Futures Pricing: Advanced

  24 questions
• Topic 03

  Interest Rate Swaps: Valuation

  24 questions
• Topic 04

  Currency and Equity Swaps

  24 questions
• Topic 05

  Advanced Options Strategies

  25 questions
• Topic 06

  BSM Model: Advanced Applications

  24 questions
• Topic 07

  Dynamic Delta Hedging

  23 questions
• Topic 08

  Credit Derivatives

  24 questions
• Topic 09

  Volatility Derivatives

  51 questions

A few questions from this unit, with the answer and a full explanation. The complete bank is available when you start practising.

1. In a CDS index tranche structure (e.g., CDX), which tranche absorbs the first losses from defaults in the reference pool?

   • A
     The super-senior tranche, which is specifically designed to absorb first losses as a form of enhanced protection for investors
   • B
     The equity tranche (e.g., 0–3% attachment point), which absorbs losses first and therefore offers the highest spread
     Correct answer
   • C
     The equity tranche offers the lowest spread because it has the first-loss position and is therefore less risky than senior tranches
   • D
     The senior tranche (e.g., 7–30%), which bears the greatest credit risk because it covers the largest notional amount
   Explanation

   In a CDS index tranche structure, the equity tranche (typically 0–3% of the reference pool notional) absorbs the first losses from defaults. As the first-loss tranche, it bears the highest credit risk, offers the highest spread, and is most leveraged to defaults in the pool. The mezzanine tranche (e.g., 3–7%) is only affected after losses exceed 3% of the notional; the senior/super-senior tranche (e.g., 7–30%+) absorbs losses only after mezzanine is wiped out, offering the lowest spread and the highest credit quality.

2. A collateralised 5-year interest rate swap is valued by discounting projected cash flows at the OIS rate. If an otherwise identical uncollateralised swap were entered instead, how would the discount rate differ and what additional valuation adjustment would apply?

   • A
     The uncollateralised swap would have a higher fair value than the collateralised swap because the counterparty bears more risk and demands a higher present value of expected cash flows.
   • B
     The uncollateralised swap would be discounted at a rate higher than OIS to reflect counterparty credit risk; additionally, a credit valuation adjustment (CVA) would be subtracted from the value to account for the possibility of counterparty default.
     Correct answer
   • C
     The uncollateralised swap would be discounted at the LIBOR/SOFR rate rather than OIS, because uncollateralised swaps earn a higher return to compensate for the additional credit risk.
   • D
     The uncollateralised swap would be discounted at the overnight repo rate, which approximates OIS and is used for all bilateral OTC derivatives under standard ISDA credit support annexes.
   Explanation

   For a collateralised swap under a CSA, the collateral earns/pays the OIS rate, so the appropriate discount rate is OIS — very close to the risk-free rate. For an uncollateralised swap, the counterparty bears the risk of default by the other party. Two adjustments arise: (1) the discount rate may be adjusted upward to reflect the higher funding cost; and (2) a CVA (credit valuation adjustment) is subtracted from the risk-neutral fair value to reflect expected losses due to counterparty default. If the bank itself might default, a DVA (debt valuation adjustment) is also added. The CVA/DVA framework was developed post-GFC and is now standard practice under IFRS 13 for OTC derivatives.

3. When the continuous dividend yield on a stock increases, what happens to the European call option price under the dividend-adjusted BSM model?

   • A
     The call price is unaffected, because the dividend yield cancels out in the d₁ and d₂ formulas
   • B
     The call price rises by the amount of the dividend yield multiplied by the option's notional value
   • C
     The call price decreases, because the effective underlying price S₀e^{–δT} falls as δ rises
     Correct answer
   • D
     The call price increases, because higher dividends signal stronger corporate profitability
   Explanation

   A higher continuous dividend yield δ reduces the adjusted spot S₀e^{–δT} used in the BSM formula. Because call value increases with the underlying price, a lower effective spot reduces call value. Additionally, a higher δ lowers d₁ (the numerator r – δ + σ²/2 decreases), reducing N(d₁) and therefore the call price further. Conversely, put prices increase when δ rises. This is economically intuitive: dividends reduce the stock's expected price appreciation, hurting call buyers.