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The document examines the claim that an option’s delta approximates its probability of expiring in the money. In the Black–Scholes framework, the answer connects delta to the risk-neutral probability of an in-the-money expiry, with an adjustment related to…
The document explains how open interest relates to long and short positions in options and other derivatives. Because each contract has both a long side and a short side, open interest can be counted from either side: the number of open longs equals the…
The document explains how to combine volatility estimates from consecutive periods. If returns across the periods are uncorrelated, their variances add, so the standard deviation over the full two-year span is the square root of the sum of the two annual…
The document explains that a ratio of the swap bid–ask spread to the bond bid–ask spread is not a standard bond-versus-swap spread measure. Instead, the appropriate definition depends on the comparison being made and the desired treatment of the bond’s cash…
The document addresses how to estimate standard errors for GARCH parameters when fitting the model by maximum likelihood. It points to the Bollerslev–Wooldridge robust inference approach and notes that the fGarch package supports it through its…
The document considers negative spreads produced by sector spread estimates or stressed credit curves, and whether they should be converted to zero default probability. It starts from a simple spread-to-default-probability approximation based on recovery,…
The answer addresses how to interpret apparent extreme kurtosis in positive accounting ratios such as inventory turnover and inventory days. Its main point is that ratios can have distributions without finite means or variances, in which case conventional…
The document explains how to price a European call under Merton’s jump-diffusion model. A Black-Scholes calculation conditioned on a fixed number of jumps is only one component of the price; the full value averages those conditional prices across all…
The document outlines a simple Monte Carlo approach to valuing the wildcard option in Treasury futures. It proposes sampling late-day changes in the cheapest-to-deliver bond during the delivery period, then evaluating each day whether exercising the wildcard…
The document considers how to estimate an option’s implied volatility at a target maturity using options observed at nearby expiries. Its response recommends estimating an at-the-money volatility term structure rather than holding an arbitrary strike fixed…
The discussion explains that pegged orders do not necessarily retain first-in-queue priority when prices move. Queue handling depends on the exchange’s order type and matching rules; traders should check venue documentation, especially for time priority and…
The discussion considers how a bond dealer who cannot sell short might adapt a market-making strategy designed for dealers with two-sided inventory flexibility. Its central argument is conditional: if a long-only dealer already holds enough inventory to…
The discussion addresses building a daily indicator for which Eurozone government bond is cheapest to deliver against a bond futures contract, for use in a repo-rate panel regression. It gives a Bloomberg Excel history query for the futures CTD identifier…
The discussion asks how to change from a physical probability measure to a risk-neutral measure when an asset follows an additive-noise Ornstein–Uhlenbeck-style process. It distinguishes this specification from geometric Brownian motion, where the diffusion…
This discussion considers whether quasi-Monte Carlo (QMC) can help price path-dependent derivatives and how to speed up Monte Carlo simulations. It explains that an option price is an expectation over risk-neutral paths, so QMC can in principle be used to…
The document explains why an equity index futures price can be below the expected future level of the index. Under the stated setup, the expected index value reflects investors’ required expected return, while the futures price reflects the risk-free rate…
The discussion explains that a linear factor asset-pricing model can, in principle, be applied to any asset return, including an individual stock. In practice, single-stock factor betas estimated from time-series regressions can be imprecise because company…
In QuantLib, the tenor passed to a Schedule specifies the spacing used to generate dates between the schedule’s start and end dates. The discussion applies this to a floating-rate bond that references quarterly EURIBOR but pays every two months: the index…
The document discusses how to estimate the coefficient in a square-root model of equity market impact. Suggested approaches include regressing realized price moves against order size relative to volume, checking a log-log plot for square-root scaling, and…
The document explains how an at-market overnight index swap fixed rate is chosen so the swap has zero value at inception. Its floating leg compounds daily overnight rates, while the fixed leg pays the agreed rate according to the contract schedule. Under the…
The post considers lag-one sample autocorrelation in daily stock log returns and asks when its scaled estimator is asymptotically standard normal under a model with normally distributed returns. It seeks a reference for the assumptions that justify this…
The discussion contrasts European call and put prices as maturity changes. It gives an arbitrage argument that, under a positive interest rate, a call with a longer maturity cannot be cheaper than an otherwise identical shorter-dated call: if it were, buying…
The document explains the rate-unit convention for fitting Nelson–Siegel–Svensson curves to spot, forward, or discount rates. Its answer states that rates should be entered as decimals, such as 0.05 for a quoted five percent, rather than as whole percentage…
The document clarifies a distributional result for the Cox–Ingersoll–Ross short-rate model. Conditional on the current rate, a scaled future rate has a noncentral chi-square distribution; the rate by itself is not generally described by that same…