คลังความรู้

The document asks how to roughly estimate term premia at the long end of a bond curve, including for a market such as Brazil. It presents two approaches: regress the ACM ten-year term premium on several US yields, or use differences between distant forward…

The document describes a question about Levy's moment-matching approximation for Asian options under geometric Brownian motion. When some monitoring points have already been observed, the method adjusts the strike using the observed average and the share of…

The document asks whether stock price paths can be simulated with different models while holding the initial price and historical mean and standard deviation fixed. It names geometric Brownian motion (GBM), Merton jump diffusion, and Heston stochastic…

The document explains why yield-curve construction often interpolates discount or forward rates rather than observed par swap rates. Its central point is that forward rates are more differentiated quantities: par rates aggregate information across periods,…

The document compares SOFR and three-month LIBOR as indicators of credit risk. SOFR is based on secured overnight borrowing, while LIBOR included unsecured bank credit and term liquidity premia. Futures on both rates offer exposure to expected future rates,…

The document examines a repeated fair coin toss game with a broker taking a fee on every toss. It compares an estimate attributed to Victor Niederhoffer with a binomial calculation: over 200 tosses, a player must get more than 120 heads to finish ahead after…

The discussion considers default counts in a loan portfolio when each loan has a specified marginal default probability and defaults may share a common latent macro factor. One answer standardizes a shared-factor Gaussian construction to preserve the…

The discussion estimates the one-day profit and loss of a short call when the underlying moves sharply. The answer first assumes the position is delta hedged, so the starting portfolio has no first-order exposure to the spot move. It then treats the stated…

The discussion asks how to describe the sampling distributions of estimated autoregressive and moving-average coefficients in an ARMA-GARCH model. The answer gives the standard asymptotic result: under suitable assumptions, parameter estimates are consistent…

The discussion examines whether European stock portfolio returns should be converted to euros before regression against Fama-French factors reported in dollars. It first points out that a portfolio of ten high book-to-market stocks is not constructed like…

The document explores delta and vega hedging, exotic-product risk, and pricing when a derivative references an investment fund. The question highlights practical constraints: fund shares may be difficult or impossible to short, listed options may be…

The document asks how the U.S. Quote Rule and Limit Order Display Rule apply to broker-dealers that serve both as agents for clients and as dealers. The underlying concern is a potential conflict: a firm might favor its own trading interest over a customer’s…

The document asks what the number of independent forecasts, N, means in the Fundamental Law of Active Management, commonly expressed as information ratio equal to information coefficient times the square root of N. It quotes a definition that describes N as…

The document asks which securities offer options expirations more often than monthly, motivated by a strategy of buying near-the-money calls when little time value remains close to expiration. It notes that many U.S. stock options expire on the third Friday…

The example shows how an incomplete one-period trinomial market can produce multiple risk-neutral probability distributions and a range of prices for a European call. With three possible stock outcomes but only the probability-sum and discounted…

The discussion outlines factors for selecting an execution management system and aggregating fragmented FX liquidity. It compares ECNs and bank channels in terms of currency-pair strengths, liquidity, fees, technology, and available execution algorithms. It…

The discussion clarifies which expiry to use when applying a Black-style model to an option on a VIX future. It says to use the option’s exchange-published expiration date, measured from the valuation date, rather than the maturity of the underlying futures…

The document asks how to identify, from a stock universe, the three names likely to produce the highest premium for a worst-of put. Its payoff depends on the weakest normalized asset outcome at maturity, so the question concerns both individual price…

The document considers whether shorting an out-of-the-money option and hedging only when the underlying reaches its strike can reproduce the option payoff or cap losses at the premium received. It describes a stop-loss/start-gain approach: the hedge is…

Seasonally adjusted (SA) data remove recurring seasonal patterns from a time series. Seasonally adjusted annual rate (SAAR) data do that as well, then express the measurement as an annualized amount or pace. For a monthly level, the annualized figure scales…

The exercise asks whether the reciprocal of an asset price can itself be the arbitrage-free price of a traded derivative, and how to value a claim paying the reciprocal at maturity. Its attempted valuation uses risk-neutral discounted expectation under…

The question considers a process defined by integrating time multiplied by the increments of a geometric Brownian motion, and asks for its expectation and variance. The response applies the product rule to the product of time and the asset process,…

This discussion surveys Python approaches to portfolio construction, focusing on mean-variance and minimum-variance optimization. It points to convex optimization packages that can solve quadratic portfolio problems, with higher-level interfaces for…

The document describes a one-expiry SPX implied-volatility calibration using the SSVI parameterization. The initial implementation produced implausible estimates when fitting market option prices, and the author also found that the fitting objective had…