คลังความรู้

The question concerns regressions linking Bitcoin prices with daily Reddit post counts and sentiment. The author reports that price appears integrated while the social measures appear stationary, yet the series show strong correlation, high regression fit,…

The answer shows how to test a laddered option payoff for mispricing by expressing it as a portfolio of simpler calls. It first represents the payoff across strike-defined regions, then rewrites it using call payoffs that activate above each strike. For the…

The discussion addresses how to estimate an option’s vega, volga, and vanna by repricing after perturbing the volatility input. When a product depends on an entire Black variance surface, replacing it with a single constant volatility can be unsuitable for…

This discussion derives the first-order condition for a risk-neutral investor who maximizes expected portfolio return subject to a bound on return variance. It clarifies that the constraint in the question limits standard deviation, so squaring it gives an…

The document questions whether a nearby-versus-next-month futures spread is a stable mean-reverting series suitable for high-frequency arbitrage. It challenges the assumption that the spread should track an interest-rate benchmark, explaining that futures…

The document clarifies that a risk-neutral probability measure is not generally a special case of an invariant measure. A risk-neutral measure can be obtained through a change of probability measure that adjusts for selected market prices of risk, so that…

A call option on a forward gives its holder the right to enter a forward contract at the option’s expiry. Whether exercise is worthwhile depends on the forward price at that time relative to the strike. The resulting exposure is to the forward contract; it…

The document explains two interpretations of the Information Coefficient in the Fundamental Law of Active Management. One measure converts the share of correct directional calls into a score; the other computes the correlation between forecast and realized…

The question defines market impact for a market order as the price difference between the first and last shares executed. It observes that, if the order book were static, the visible sell-side depth would indicate the last price reached by a buy order. The…

The note outlines a model-based route to backtesting variance and volatility swaps when direct swap data is unavailable. It uses a one-factor Bergomi setup in which instantaneous variance follows a lognormal process correlated with the asset return. In this…

The note gives a brief overview of venues and access considerations for power derivatives. Responses mention ICE and NYMEX for over-the-counter power contracts, CME as another derivatives venue for power markets, and Clearport settlements as a place where…

The note explains the difference between measuring interest-rate risk by individual tenors and measuring it on a single, undecomposed curve. For delta, rates at standard maturities can be shifted one at a time to estimate tenor sensitivities; their sum…

The document surveys research on whether cryptocurrencies differ quantitatively from currencies and other assets. It describes proposed distinctions such as decentralized transaction records, market-specific drivers, high volatility, and limited history. The…

The document derives a replication for a European chooser option, which lets its holder decide at an intermediate date whether to receive a call or a put, both expiring later. At the choice date, put–call parity expresses the put payoff as the call payoff…

The document uses monthly regressions on a benchmark market return and style factors to interpret two portfolios' return patterns. It reads coefficient t-statistics as evidence of factor exposures: both funds show market sensitivity, while the second has…

The document explains an FX swap as an exchange of currencies at spot with a later reversal, and asks how to value the remaining cash flows. Its answer emphasizes that market quotes use forward points: the forward rate is the spot rate plus the quoted…

The document describes an option-pricing problem in which volatility changes when the underlying crosses a specified barrier. It suggests this setup may represent a post-crash environment where near-term option volatility is elevated and expected to move…

The document asks why a futures price is not simply the expected future spot price, and contrasts this intuition with cost-of-carry pricing. Its answer frames futures and forwards through arbitrage-free pricing: if an asset can be bought and financed until…

The document considers how to estimate daily value-at-risk for a long option and asks whether the estimate can reflect the fact that the position cannot lose more than its premium. It contrasts a rough premium-based rule with delta-gamma VaR, which…

The document asks how to estimate the drift or mean-reversion parameter of an Ornstein-Uhlenbeck process when its long-run mean is known. It proposes expressing the process in discrete time as an AR(1) relation around that mean and fitting the autoregressive…

The document explains why fixed-rate and floating-rate bonds can require distinct curves in a pricing setup. A discount curve supplies the factors used to value a bond’s cash flows, while a forward curve estimates the reference rate that determines future…

The document derives the probability that Brownian motion is positive at a later time and negative at an earlier time. It rewrites the event using the increment from the earlier to the later time and the negative of the earlier value. These variables are…

The document addresses how a credit union might estimate the funding benefit of equity in a funds transfer pricing or risk-adjusted profitability model. The proposed calculation multiplies the target capital ratio by the loan’s risk weight and by the cost of…

The document explains how to infer an implied USD borrowing rate from EUR/USD spot and overnight forward-point quotes when borrowing dollars through an FX swap. The key correction is to compare the forward exchange rate with the same spot rate used in the…