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FRM Part I Updated
What is the timing option in Treasury bond futures delivery, and how does the short exploit it during the delivery month?
The timing option lets the futures short choose when during the delivery month to deliver. The decision hinges on net carry: positive carry favors late delivery to capture coupon income exceeding financing costs, while negative carry favors early delivery.
How does the cheapest-to-deliver switch option work in Treasury bond futures, and when does the CTD bond change?
The CTD switch option arises because the conversion factor system imperfectly normalizes deliverable bonds. As yields move away from 6%, different bonds become cheapest to deliver, giving the futures short a valuable option to switch which bond is delivered.
How does linear interpolation work on a bootstrapped yield curve, and what artifacts does it introduce?
Linear interpolation connects known yield curve nodes with straight-line segments, producing a continuous zero curve. However, it creates discontinuous forward rates with abrupt jumps at each node, making it unsuitable for pricing forward-sensitive instruments.
How does a knock-in barrier option actually activate, and what determines its value before the barrier is breached?
A knock-in barrier option only becomes a live vanilla option once the underlying asset's price touches a predetermined barrier level. Before activation, its value reflects the probability of barrier contact and the conditional value of the resulting vanilla option.
Why did the industry shift to OIS discounting for collateralized derivatives, and how does it differ from LIBOR discounting?
OIS discounting reflects the true funding cost of collateral posted under CSA agreements. Since collateral earns the overnight rate rather than LIBOR, discounting at LIBOR overstates present values by embedding an unnecessary bank credit spread.
How is the swap rate curve constructed, and why does bootstrapping from deposit rates to swap rates matter for valuation?
The swap rate curve is bootstrapped sequentially from deposit rates, futures-implied forwards, and par swap rates. Each instrument covers a specific tenor range, and discount factors are solved iteratively so that longer-maturity values depend on all earlier ones.
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 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.
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.
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.
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 the conversion factor determine the cheapest-to-deliver bond in Treasury futures, and when does it break down?
The conversion factor prices each deliverable bond as if yields were 6%, but real yields deviate from this assumption. When yields are above 6%, the longest-duration, lowest-coupon bonds become cheapest to deliver; when yields are below 6%, short-duration bonds are favored.
What is the cross-currency basis, and why does it deviate from zero even when covered interest rate parity should hold?
The cross-currency basis is the spread above or below what covered interest rate parity predicts in a cross-currency swap. Persistent deviations arise from structural dollar funding demand, regulatory capital constraints, and balance-sheet costs that prevent arbitrageurs from eliminating the gap.
How does component VaR decompose total portfolio risk into individual position contributions?
Component VaR decomposes total portfolio VaR into additive pieces from each position. It is calculated as the position weight times its beta to the portfolio times total VaR, and all components sum exactly to total portfolio VaR.
How do you calculate a DV01-based hedge ratio using Treasury futures, and what adjustments are needed for the CTD bond?
The DV01 hedge ratio divides the portfolio's dollar sensitivity per basis point by the CTD bond's DV01, then multiplies by the conversion factor. This ensures the futures position's interest rate sensitivity matches the cash position being hedged.
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