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How does the delta-gamma approach improve VaR estimation for options portfolios compared to delta-only VaR?
The delta-gamma VaR approach captures the curvature of option payoffs that delta-only VaR ignores. By adding the 0.5 x gamma x (dS)^2 term, the quadratic approximation accounts for how positive gamma cushions losses and negative gamma amplifies them.
How should banks set Key Risk Indicator (KRI) thresholds, and what makes a KRI actionable versus merely informational?
Effective KRIs are leading, measurable, and actionable metrics with statistically calibrated green/amber/red thresholds. Threshold setting uses historical distributions, and every breach must trigger a defined escalation protocol with clear ownership and response timelines.
How do banks use scenario analysis to estimate operational risk severity, and what role do expert judgment workshops play?
Scenario analysis uses structured expert workshops with modified Delphi methods to estimate the frequency and severity of extreme operational risk events. Debiasing techniques counter anchoring, availability bias, and groupthink to produce calibrated severity distributions for stress testing and risk appetite.
What is the ILM coefficient, and how does national discretion on the ILM affect cross-border capital comparability?
The ILM coefficient determines whether internal loss data affects capital. National supervisors can set ILM = 1 (eliminating loss sensitivity), floor it at 1.0 (only allowing surcharges), or use the full formula. This discretion creates cross-border inconsistency for international banks.
What are the three components of the Business Indicator (BI), and how do absolute value adjustments prevent manipulation?
The Business Indicator comprises three sub-indicators capturing intermediation, services, and financial activities. Absolute values and max functions in the formulas prevent banks from reducing their operational risk proxy through offsetting positions or deliberate netting.
How does a credit-linked note (CLN) work, and what is the difference between funded and unfunded credit risk transfer?
A credit-linked note embeds a CDS inside a bond wrapper, providing funded credit risk transfer. The investor buys the note at par, receives enhanced coupons funded by CDS premiums and collateral yield, and bears principal loss if the reference entity suffers a credit event.
What is a decumulator, and how does it mirror the accumulator's risk profile for holders of existing stock positions?
A decumulator obligates the investor to sell shares daily at a premium to the initial price, with 2x gearing that doubles selling quantities when the stock rises above the strike. It is the mirror image of the accumulator, designed for stockholders wanting above-market exit prices while accepting rally-related opportunity costs.
How does a Target Redemption Note (TARN) work, and why does the cumulative coupon cap create early termination risk?
A Target Redemption Note automatically redeems once cumulative coupons reach a preset lifetime cap. Since coupons are typically inverse floaters, the note terminates fastest when rates are lowest, creating reinvestment risk at precisely the worst moment for the investor.
How does a range accrual note work, and what type of exotic option is embedded in its coupon structure?
A range accrual note pays coupon only for days the reference rate remains within a specified band. Each daily observation embeds a pair of digital options, making the full note a strip of hundreds of binary payoffs whose hedging is complicated by discontinuous payoff profiles near the range boundaries.
How is a principal protected note (PPN) constructed, and what limits the participation rate an issuer can offer?
A principal protected note is built by allocating investor capital between a zero-coupon bond (guaranteeing principal) and a call option (providing equity upside). The participation rate depends on how much budget remains after purchasing the ZCB, which is directly determined by interest rates.
Why is DVA (Debit Valuation Adjustment) controversial, and what are the main arguments for and against including own credit risk in derivatives valuation?
DVA is controversial because it creates accounting profits when a firm's creditworthiness deteriorates. While accounting standards require it for bilateral consistency, regulators exclude it from capital because the gains are unrealizable and create perverse incentives.
How does bilateral CVA incorporate both parties' default risk, and what role does netting play in the calculation?
Bilateral CVA equals unilateral CVA minus DVA, accounting for both counterparties' default risk. Netting agreements dramatically reduce exposures by offsetting positive and negative MtM positions, lowering both CVA and DVA calculations.
What is the wild card option in Treasury bond futures, and how does the short use the late-afternoon price window?
The wild card option lets the short declare delivery using the 2:00 PM settlement price anytime until 8:00 PM, while bonds keep trading. If prices fall during this window, the short buys cheap bonds and delivers against the locked-in higher invoice.
What is the end-of-month option in Treasury bond futures, and why does it exist after the last trading day?
The end-of-month option exists because Treasury bond futures stop trading several days before the delivery month ends, but the short can still deliver. The frozen settlement price against fluctuating bond prices creates an option the short can exploit if prices decline.
What is right-way risk, and how does beneficial correlation between exposure and counterparty credit quality reduce CVA?
Right-way risk occurs when derivative exposure decreases as the counterparty's credit deteriorates. A classic example is a gold forward with a gold miner — exposure is highest when gold prices rise, which is exactly when the miner is financially strongest.
How does cubic spline interpolation smooth the forward rate curve, and what are the potential drawbacks of spline-based methods?
Cubic spline interpolation fits third-degree polynomials between yield curve nodes with continuity constraints on first and second derivatives, producing smooth forward rates. However, splines can overshoot between widely spaced nodes and behave erratically at the long end.
What makes a risk factor non-modellable under FRTB, and how are NMRFs capitalized separately?
Under FRTB, risk factors without at least 24 annual price observations (with no gap exceeding one month) are classified as non-modellable. NMRFs receive separate stressed scenario capital charges aggregated with limited diversification, creating strong incentives to source observable data.
How does the averaging feature of Asian options reduce their cost compared to vanilla options, and what types of averages are used?
Asian options use the average underlying price over a period rather than the terminal price, which reduces effective volatility and lowers the option premium. The two main types — average price and average strike — serve different hedging purposes.
How does ISDA SIMM calculate initial margin, and what are the risk sensitivity buckets?
ISDA SIMM calculates initial margin by computing delta, vega, and curvature sensitivities across six risk classes, assigning them to currency or sector buckets, applying risk weights, and aggregating using prescribed intra-bucket and inter-bucket correlations.
What is the margin period of risk, and how does it affect collateral haircuts and exposure calculations?
The margin period of risk is the assumed duration between a counterparty's last margin payment and full portfolio closeout after default. It scales potential future exposure and collateral haircuts, with regulatory floors of 5 days for cleared trades and 10-20 days for bilateral positions.
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