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FRM Part I Updated
When should I use a lognormal interest rate model instead of Gaussian?
Lognormal models keep rates positive and match observed skew but sacrifice analytic tractability and need numerical methods...
How does a barrier note with knock-in protection create cliff risk for investors?
Barrier notes have a knock-in put that activates if the underlying breaches a barrier, creating cliff risk where small moves cause large payoff changes.
What are the most common problems when scaling VaR across time?
Three structural issues plague time scaling. First, volatility is time-varying; a ten-day horizon almost certainly spans regime shifts that a daily vol does not reflect.
Is the Ho-Lee model still relevant or just a historical stepping stone?
Ho-Lee is the simplest no-arbitrage model with no mean reversion, mostly historical but useful for pedagogy and short horizons...
What are the key components of a risk appetite statement and how does it differ from risk tolerance and risk capacity?
A Risk Appetite Statement (RAS) is a formal board-level document that articulates the types and aggregate level of risk a firm is willing to accept in pursuit of its strategic objectives.
How do buffer notes differ from principal protected notes in downside protection?
Buffer notes absorb the first X% of losses but expose the investor to declines beyond. They combine a call spread with a short OTM put.
How do I decide between 95%, 99%, and 99.9% confidence for VaR?
The confidence level answers 'how often am I willing to breach VaR?' A 95% daily VaR is breached on average 13 times per year; 99% once every 100 trading days.
What's the advantage of the Hull-White one-factor model over Vasicek?
Hull-White makes the long-run mean time-dependent to exactly match the observed curve, enabling no-arbitrage calibration...
How do you design effective Key Risk Indicators (KRIs) and what distinguishes a good KRI from a bad one?
Key Risk Indicators (KRIs) are quantitative metrics that provide early warning signals of increasing risk exposure or weakening controls. They sit between risk identification and loss events.
What is a callable yield note and how does the issuer's call right affect pricing?
A callable yield note embeds a short Bermudan call sold by the investor. The enhanced coupon compensates for negative convexity and reinvestment risk.
Why can we scale VaR using the square root of time, and when does it fail?
Square-root-of-time scaling rests on three assumptions: returns are independently distributed, returns have constant volatility, and the mean is negligible over the horizon.
Why does the CIR model prevent negative rates and how does it differ from Vasicek?
CIR replaces constant volatility with sigma*sqrt(r), which vanishes at zero, preventing negative rates under Feller...
How do firms use internal and external loss data for operational risk management?
Loss data is the empirical backbone of operational risk measurement. Without reliable loss data, all the models and frameworks are built on guesswork. The FRM curriculum emphasizes both internal and external data sources.
How does a range accrual note pay coupon based on an index staying within a range?
Range accruals pay coupon based on days inside a reference range. Structurally they are strips of digital options, winning when rates are stable.
What is the difference between absolute VaR and relative VaR?
Absolute VaR measures the potential loss in dollar terms from the current portfolio value, while relative VaR measures the loss relative to the expected value at the horizon.
How does mean reversion work in the Vasicek model and what are its limitations?
Vasicek uses dr = a(b - r)dt + sigma dW with mean reversion speed a, long-run mean b, and constant volatility...
What's the difference between scenario analysis and RCSA in operational risk management?
Scenario analysis and RCSA are both qualitative tools in the operational risk toolkit, but they serve different purposes, involve different participants, and produce different outputs.
How does an autocallable note work and when does it redeem early?
Autocallables pay contingent coupons and redeem early if triggers are met. They are priced via Monte Carlo and perform best in sideways markets.
Can you explain affine term structure models in plain language?
Affine models express the short rate as a linear combination of latent factors, yielding closed-form bond prices...
How does a reverse convertible note enhance yield and what is the investor actually selling?
A reverse convertible is a high-yield bond plus short put. The investor effectively sells downside insurance on a single stock to fund the enhanced coupon.
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