নলেজ লাইব্রেরি

The post asks whether QuantLib’s Longstaff–Schwartz Monte Carlo engine for American options can use non-Gaussian random draws, such as Student-t variates, while pricing under a Black–Scholes–Merton process. The author considers changes to distribution and…

The problem asks whether a finite linear filter of weak white noise has a time-invariant mean and autocovariance. The attempted proof correctly aims to use the fact that the input process has a constant mean and covariance structure, but it incorrectly…

The post questions why Micro E-mini S&P 500 futures expiring in June 2021 were quoted below the March 2021 contract, despite the author’s expectation that later expiries should cost more to avoid arbitrage. It notes that the S&P 500 is a total return index…

The document explains why a stochastic-volatility model writes wealth changes in terms of the dollar amount invested in a risky asset rather than the asset price itself. If an investor commits an amount to the asset, the number of units held is that amount…

The document surveys reasons a quantitative team might choose R for financial data modeling instead of spreadsheets or conventional statistical packages. It emphasizes reusable scripts, access to packages that implement statistical methods, flexibility for…

The document considers how to estimate daily risk-free returns for calculating excess returns on individual stocks and a broad equity market. It discusses using a three-month Treasury bill yield as a proxy, and raises a key data question: quoted yields may…

The document compares a dividend swap with a dividend future when both provide exposure to dividends through a stated strike or entry price. In the example, a long position entered at 100 gains when the dividend outcome or futures price rises to 102, but the…

The document outlines a parametric approach to option value-at-risk using a first-order Taylor approximation. It estimates option price changes as the sum of delta exposure to underlying-price changes and vega exposure to implied-volatility changes. Under…

The document uses a delta-hedged option approximation to estimate the underlying price move needed to offset one day of time decay. Setting the approximate gamma gain equal to theta decay gives a break-even move proportional to the square root of twice the…

The document contrasts the end-of-month delivery option in Treasury futures with the switch option before and after futures trading ends. Before expiry, the futures price remains variable and is driven mainly by the converted price of the cheapest-to-deliver…

The document explains one direction of the fundamental no-arbitrage result: if discounted asset prices admit an equivalent martingale measure, an arbitrage strategy cannot exist. Under that measure, the discounted value of a self-financing strategy is a…

The document challenges the claim that demand is generally greater for out-of-the-money and in-the-money options than for at-the-money options. The responses distinguish trading volume from volatility-smile explanations: near-the-money options are described…

The document asks how Itô’s lemma can help derive Clark’s representation for a smooth, bounded function of Brownian motion at a fixed horizon. The stated formula expresses the terminal function value as its expectation plus a stochastic integral whose…

The document considers how to use an option on a zero-coupon bond to protect a minimum yield. Its response translates a yield threshold into an approximate bond-price strike, then explains the position direction: selling a call at that strike limits the…

The document asks how to estimate the expected return of a broad stock index when calculating the market price of risk in a change from real-world to risk-neutral dynamics. It presents the relationship between that price and an asset’s correlation with the…

The document asks where to obtain real-time foreign exchange data at intervals shorter than one minute, including buy and sell quotes and recent trades. It notes that the questioner’s searches of two data services found a one-minute minimum, then gathers…

The document explains why effective interest formulas add one to a periodic rate, multiply the resulting growth factors, and subtract one at the end. The added one represents retaining the original principal as well as earning interest during each period.…

The document asks how to apply the FDR+ method to select trading rules that appear to outperform. It says the author has computed p-values using a stationary bootstrap, following a cited study, but provides no worked calculation, code, or detailed definition…

The document examines whether gross exposure divided by capital is a useful definition of portfolio leverage. It points out that this measure omits cash and can overstate risk when offsetting holdings are highly correlated, then derives a risk-based…

The document examines the parallel-shift assumption behind aggregating bond durations into a portfolio duration. It distinguishes shifts in the zero-rate curve from equal changes in the yields to maturity of individual coupon bonds, noting that coupon-bond…

The document examines a common first-order approximation for the premium of an FX risk reversal: multiply at-the-money option vega by the risk reversal in volatility points. It explains that the approximation should compare the market-priced call and put…

The document explores whether investor reallocation can explain spillovers between asset returns. It starts from a mean-variance utility model and derives an unconstrained relationship between an investor’s holdings in two assets: the sensitivity of one…

The document examines the rare case where extending the maturity of a low-coupon bond trading at a deep discount can reduce its Macaulay duration. Duration is a present-value-weighted average payment time, so the maturity date alone does not determine…

The document explains a step in proving that an integrable stochastic process with centered, independent increments is a martingale. For times s before t, the increment from s to t is independent of information available through time s, so conditioning that…