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FRM Part I Updated
What are the upper bounds on call and put prices?
Call upper bound: c <= S. European put: p <= K*e^(-rT). American put: P <= K...
How do contract size and notional value relate in futures?
Contract size is the exchange-defined quantity of the underlying per contract. Notional value is contract size times current price — the economic exposure you carry.
What are the key specifications I need to know for a futures contract?
Futures contract specifications are the standardized terms the exchange defines so every contract is fungible. Six elements matter most: underlying asset, contract size, delivery month, price quotation, tick size, and delivery terms.
What is Fitch's approach to corporate ratings and how is it different from Moody's/S&P?
Fitch publishes 'Navigator' rating reports for each issuer — a one-page visual scorecard showing how key factors map to the rating. The framework uses four pillars similar to S&P: Sector Risk Profile, Operating Environment, Company Profile, and Financial Profile...
What is contraction risk and why does it hurt MBS investors when rates drop?
Contraction risk is accelerated principal return when rates fall and borrowers refinance. Reinvestment at lower yields caps the MBS's upside, creating negative convexity.
Why do interest rate models use trinomial trees instead of binomial?
Trinomial trees add a third branch at each node, giving more flexibility for matching mean-reverting dynamics common in interest rates...
What's the best way to estimate realized volatility from high-frequency data?
Each estimator trades bias against variance and microstructure noise. Close-to-close is unbiased but noisy; Parkinson uses daily high-low and is 5x more efficient.
What information appears on a credit bureau report and how do lenders use it?
Bureau reports contain identifiers, trade lines, public records, inquiries, and collections. Lenders use both the composite score and derived attributes for application scoring.
What is a commercial credit risk model (KRM) score and when should I use it?
Commercial scores like RiskCalc, PAYDEX, SBSS, and Intelliscore use financial statements and trade data rather than consumer bureau files, and typically output PDs directly.
What are the lower bounds on European call and put prices?
Lower bound: c >= max(S - K*e^(-rT), 0) for calls, derived via replicating portfolios...
How do I construct a synthetic call from a put?
Synthetic call = long put + long stock + short bond (borrow PV of K)...
How does S&P's corporate rating methodology differ from Moody's?
S&P uses a two-step framework that is more explicit than Moody's. Step 1 is the Business Risk Profile (BRP), which combines Country Risk + Industry Risk + Competitive Position. Step 2 is the Financial Risk Profile (FRP)...
What does gamma actually tell a hedger, and how is it used in practice?
Gamma measures how fast delta changes. Long-gamma books profit from realized volatility via rebalancing; short-gamma books bleed when markets move.
How does the PSA prepayment model work and why is 100 PSA the benchmark?
PSA standardizes prepayment speed. 100 PSA ramps CPR from 0.2% to 6% over 30 months. Multiples like 165 PSA scale both the ramp slope and plateau proportionally.
How do I price an American put option using a binomial tree?
American put pricing on a binomial tree requires checking the early exercise condition at every node during backward induction...
How is the VIX actually calculated from option prices?
The VIX is a model-free estimate of 30-day risk-neutral variance, computed as a weighted sum of out-of-the-money SPX option prices weighted by 1/K^2.
How does KMV-Moody's EDF differ from the plain Merton model?
KMV uses short-term debt plus half long-term as the default point, iterates for asset value, and maps DD to empirical EDF from historical defaults — not N(-DD).
How do I calculate Merton model distance to default step by step?
DD = [ln(V/D) + (r - 0.5 sigma^2)T] / (sigma sqrt(T)). PD = N(-DD) under the risk-neutral measure.
How do I construct a synthetic put from a call?
Synthetic put = long call + short stock + long bond paying K, from rearranging parity...
How do dividends create a case for early exercise of American calls?
Dividends create early-exercise cases for American calls when D > K*(1-e^(-rt))...
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