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FRM Part I Updated
How do I calculate delta for a European call step by step?
Delta = N(d1) for a European call. Walk through a Brindle Motors example: d1 = 0.3247 gives delta ≈ 0.626, so hedge 1,000 calls with 626 short shares.
How is a pass-through security structured and what does the investor actually own?
A pass-through gives investors a pro-rata undivided interest in a mortgage pool. WAC is the gross mortgage rate; the pass-through rate is WAC minus servicing and guarantee fees.
How is the variance risk premium different from the volatility risk premium?
The variance risk premium is the gap between the variance swap rate K_var and expected realized variance. The volatility risk premium is the same idea in vol units.
What is the Altman Z-score formula and how do I interpret it for manufacturers?
Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5. Safe zone above 2.99, distress below 1.81.
How do FICO credit scoring models work for consumer lending?
FICO scores range from 300 to 850 and are built from five weighted components: payment history 35%, amounts owed 30%, length of history 15%, new credit 10%, and credit mix 10%.
When is it optimal to exercise an American put early?
American puts CAN be optimal to exercise early because the strike earns interest immediately...
How does put-call parity work for European options and why can't it be violated?
Put-call parity states C + PV(K) = P + S because both sides replicate max(S_T, K) payoff...
How do rating agencies actually assign a rating to a corporate bond issuance?
The rating process is a structured engagement. Consider Meridian Logistics Inc., a mid-size freight operator issuing a $400M senior unsecured note. The steps are engagement, information submission, management meeting...
What are the option Greeks and why does FRM emphasize each one?
Greeks quantify how an option's value moves when a single input shifts. Delta, gamma, theta, vega, rho each measure a different sensitivity used for hedging and risk limits.
What exactly is a mortgage-backed security and how does the cash flow structure work?
A mortgage-backed security (MBS) is a bond whose cash flows come from a pool of residential mortgages. Unlike corporate bonds, MBS are amortizing, carry prepayment risk, and pass through payments net of servicing and guarantee fees.
What is the volatility risk premium and why does it exist?
The volatility risk premium (VRP) is the persistent gap between option-implied volatility and subsequently realized volatility on the underlying. Empirically, 30-day S&P 500 implied vol averages roughly 3-4 vol points above realized.
When should I use delta-gamma VaR instead of delta-normal?
Delta-gamma VaR extends the linear delta approximation with a quadratic gamma term, capturing curvature in option payoffs.
How is delta-normal VaR calculated for a multi-asset portfolio?
Delta-normal VaR linearizes positions using their deltas (first-order sensitivities) to underlying risk factors, then treats the risk factor returns as jointly normal.
How do mixture distributions improve VaR estimates?
A mixture distribution combines two or more normal (or other) distributions with weights that sum to one.
When should I use lognormal VaR instead of normal VaR?
Lognormal VaR models the price level as lognormal, equivalently log returns as normal, which enforces positive prices and a skewed loss distribution.
What is a shark-fin note and why is it called that?
Shark-fin notes pay participation up to a barrier, then collapse to a small rebate if breached. Structurally a bond plus up-and-out call plus digital rebate.
How does Student-t VaR handle fat tails compared to normal VaR?
The Student-t distribution has a parameter nu (degrees of freedom) that governs tail thickness: lower nu means fatter tails.
What does it mean to calibrate an interest rate model to no-arbitrage conditions?
No-arbitrage calibration matches model prices to benchmark instrument prices across three tiers: bonds, vanilla vols, exotics...
What are structured deposits and how do they differ from regular CDs?
Structured deposits combine FDIC-protected principal with market upside but have zero coupon, caps, and opportunity cost vs. regular CDs.
Can you walk me through the normal VaR formula with a concrete example?
For a portfolio with mean return mu and standard deviation sigma over the horizon, the normal VaR at confidence level c is VaR = -(mu + z * sigma) * V.
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