คลังความรู้

The document raises a measurement question for a volatility risk premium strategy using options on a futures contract. The underlying future expires annually, while options are available at quarterly expiries. The proposed measure is to compare the implied…

The question considers how to invest a large sum that will arrive at the end of year two and remain invested for two years. It provides continuously compounded zero-coupon yields across maturities and asks which approach offers the safest real-term…

The document explains how interest is handled when one party posts a US Treasury security as collateral for a derivatives contract. Unlike cash collateral, which may be returned with an explicit interest payment, securities collateral generally does not…

The document considers whether a noisy Ornstein–Uhlenbeck process with a moving reference band and a cooldown period has a financial interpretation. The band is reset when the process exits it, while a dead period prevents another update for a fixed time.…

The document distinguishes a decline in Federal Reserve mortgage-backed security holdings from the broader meaning of tapering. It explains that tapering generally refers to slowing the pace of asset purchases. A reduction in the Fed’s monthly MBS buying…

The document examines a mathematical issue in deriving the expected value of the Cox–Ingersoll–Ross short-rate process. Applying Itô’s lemma to an exponentially scaled rate gives a drift term that leads to the familiar expected-rate expression, provided the…

The document explains how to estimate pre-settlement risk, or potential future exposure (PFE), for a five-year interest rate swap. Although its question asks whether payments from the counterparty should be constant, the answer clarifies that exposure is the…

The document considers whether a continuously traded energy market can be modeled with diffusion and an auction-based market with occasional jumps. The proposed approach is to build a separate jump-diffusion process for each market, allowing the auction…

The document explains why a swap-based reference curve can be suitable for pricing USD interest-rate instruments, while emphasizing that the spread measure often matters more than the curve choice. It distinguishes the I-spread, which compares a bond’s yield…

The document addresses how to interpret implied volatility for commodity options whose delivery or settlement reflects prices over a period, as in power markets. Its central point is that implied volatility is tied to the underlying specified in the option…

The document compares two portfolio optimization objectives: expected return penalized by variance, and expected return penalized by standard deviation. It derives a parameter mapping, δ = η divided by the portfolio’s standard deviation, that makes their…

A box spread combines two option conversions at different strikes and the same expiration. The underlying positions offset, while the option premiums create an initial cash inflow or outflow against a fixed settlement value. The answer describes the…

The discussion compares two ways to estimate annual return skewness and kurtosis from a long series of daily continuously compounded returns. One approach is to aggregate daily returns into annual returns and calculate the statistics from those annual…

The document considers why options on the same stock and expiration can show sharply different implied volatility readings, including around a stock split. It points to quote quality and calculation choices as likely explanations rather than evidence of a…

The document discusses unstable coefficient estimates when returns-based style analysis uses many correlated indices or factors. Suggested tools include ridge and lasso regression, which add penalties to coefficient estimates; lasso can also encourage factor…

The document considers why a financial firm might seek patent protection for a model, but its answer focuses narrowly on risk vendors. Such vendors may need to disclose their methods to customers, which can make proprietary ideas easier for competitors to…

The document explains why interest-rate indices with different tenors can have different values and why derivatives referencing them may require separate curves. It attributes part of the spread between six-month and three-month LIBOR to the additional bank…

The document compares ways to value constant-maturity swap (CMS) products, focusing on how an annuity mapping function and convexity adjustment account for the change of measure. One approach approximates the expected mapped swap rate with a second-order…

The document distinguishes return measures according to their use. To summarize a monthly portfolio series as an annual growth rate, it recommends compounding the simple monthly returns and converting that compounded growth into an annualized simple return.…

The document considers whether the spread between SOFR and US Treasury rates can serve as a credit-risk indicator analogous to the LIBOR–Treasury TED spread. Its central point is that a negative SOFR spread should not, by itself, be interpreted as evidence…

The document gives a simple way to estimate the interest-rate sensitivity of a zero-coupon bond. It compares the present value of the bond at the current yield with its present value after increasing the yield by one basis point. The difference is used as…

The document explains two order status messages that indicate trading has ended for an order. An expired status can apply when a Good Till Date order reaches its stated expiry or when a Good Till Cancel order reaches a broker’s maximum age. That age can vary…

The document considers whether two observed option-implied distributions, at an early expiry and a later expiry, can reveal the return distribution over the interval between them. It expresses the total log return as the sum of an early-period return and a…

The document examines whether pairwise dependence measures such as correlation, Kendall’s tau, or tail dependence can replace covariance in a quadratic portfolio risk calculation. Covariance has a specific justification: for portfolio returns, the quadratic…