নলেজ লাইব্রেরি

The document examines an optimization formulation for an equal risk contribution portfolio. It describes first minimizing portfolio volatility over nonnegative asset allocations subject to a lower bound on the sum of log weights, then asks whether…

The document considers choosing a call option when a stock’s terminal price is forecast to be uniformly distributed over a specified range. Assuming the available calls are priced with the Black–Scholes model, the answer recommends the lowest available…

The document asks whether a claim’s price, computed as an expectation under the risk-neutral measure, can be used directly to construct a replicating strategy by holding its derivative with respect to the stock price. The claim pays the larger of a fixed…

The document considers simulating defaults in a pool of mortgage loans whose principal declines through scheduled payments and nonrandom prepayments. The author proposes modeling the conditional default rate with a nonnegative, mean-reverting square-root…

The document addresses confusion about how an Ornstein–Uhlenbeck (OU) process can be stationary when its mean and variance may change over time. One response points to a distributional condition involving increments over time intervals of equal length and…

The document asks how to calculate the standard deviation of a three-security portfolio when the asset weights, individual expected returns, standard deviations, and pairwise correlations are known. The accepted response gives the core method: combine the…

The document explains why a portfolio’s cumulative return generally differs from multiplying the cumulative returns of its component assets. For each period, the portfolio return is the sum of the weighted asset returns. Multiplying the assets’ gross returns…

The example explains why a QuantLib price for a fixed-rate bond can differ from a hand calculation. It first checks the generated cash flows and finds that the semiannual coupon schedule is as intended. The initial zero curve, however, interpolates from a…

The discussion considers an open term loan that pays monthly interest and returns principal when closed. Because either the lender or borrower can end the loan, its remaining cash flows depend on interest rates and on each party’s decision to call or repay.…

The question considers an option that pays the difference between two stock prices at maturity only if stock A has remained above stock B throughout the contract. The accepted response reframes the condition by using stock B as the numeraire. In units of B,…

The discussion compares ways to set floating cash flows for interest rate swaps after LIBOR, whose fixing was known at the start of an accrual period. It distinguishes forward-looking term rates from backward-looking overnight risk-free rates compounded over…

The discussion explains why executions recorded for an order in LOBSTER data can share the order’s submitted limit price. A buy limit order resting at 100 may be filled by incoming sell orders at that price, or it may execute against several resting sell…

The document describes two ways to translate a government bond futures position into cash-bond exposure. A simple approach identifies the current cheapest-to-deliver bond and scales its value and risks by the inverse of that bond’s conversion factor. This…

The document explains how to value a European put that knocks in at a lower barrier and knocks out at an upper barrier. It expresses the payoff using the terminal put payoff and indicators for whether the underlying has crossed the lower barrier and remained…

The document asks whether the effective parameters in a time-decay SABR model can be expressed by one closed-form formula across all values of the decay start time. It presents two results from Sander Willems’s backward-looking SABR work: one for decay…

The document explains that there is no standard rule for how many past days to use when estimating historical volatility. It distinguishes historical, or realized, volatility from implied volatility: option prices reflect the market’s view of future…

The note explains that options on volatility control indexes exist, even though they may not appear as exchange-listed contracts. It says these options are generally embedded in structured notes and are mainly traded over the counter. This provides a reason…

The note distinguishes the Federal Funds rate from the Overnight Index Swap rate when analyzing USD interest rate swaps. The Federal Funds rate is an overnight rate, while an OIS rate represents the fixed leg of a swap against compounded daily Federal Funds…

The note asks whether portfolio gamma and vega, like delta, can be calculated by summing the Greeks of each position. The answer says that in linear valuation models, prices and their Greeks add across positions. It specifically identifies Black–Scholes as a…

The note discusses numerical instability when using the Bjerksund–Stensland 2006 option pricing model at very low volatility, especially when solving for implied volatility on out-of-the-money options. It offers a practical parameter choice: use a minimum…

The document compares ways to obtain historical company fundamentals for multiple stocks in machine-readable formats. The original request prioritizes several years of data, broad international coverage, index-level or identifier-based retrieval, and sample…

The document describes calculating Black–Scholes delta and vega in R for a sample of executive compensation contracts containing multiple options. The author derives the Black–Scholes call sensitivities and reports that computed vega values are zero,…

The document describes an attempt to find directional patterns in second-by-second market depth data using dimensionality-reduction and classification methods. A UMAP visualization appeared to separate observations labeled by subsequent price direction, but…

The document considers how to analyze price histories for a company with no trading record by using similar firms whose shares trade thinly across two exchanges. Stale prices and differing market conditions make direct time-series modeling difficult, and the…