คลังความรู้

This note considers how to model future spot when log returns are assumed to follow a Student-t distribution rather than a Gaussian one. It highlights a key theoretical problem: the Student-t distribution lacks a moment-generating function, so the…

This note derives the delta of a European cash-or-nothing call that pays when the terminal asset price exceeds a strike. Under the Black–Scholes framework, the option value is the discounted probability of finishing above the strike, and differentiating it…

This note explains why a delta-hedged position that is short options can lose when the underlying price moves. A zero net delta at the hedge point describes the position’s immediate sensitivity; it does not mean the option price falls when spot rises. For a…

This note examines when a floating rate note (FRN) prices at par and how its rate exposure depends on the relation between its coupon index and discount curve. With matching forecast and discount curves, the floating coupons telescope against the discounted…

The document answers whether a country-specific market risk premium and inflation rates belong in a currency forward-rate calculation. Under covered interest rate parity, the forward exchange rate is determined by the spot exchange rate and the two…

The document explains what a strip of Eurodollar futures can imply when its quarterly rates are compounded over a one-year period. The resulting rate represents a December-starting one-year compounded three-month LIBOR forward, and is closely related to a…

The document considers how to estimate a stochastic process value between two simulated time-grid points for an SDE with drift and diffusion. Straight-line interpolation may give an intermediate value, but it does not preserve the process’s random evolution.…

The document explains how the risk-aversion coefficient in mean-variance utility affects portfolio choice. A low coefficient places less weight on variance and permits greater risk exposure; a high coefficient penalizes risk more heavily. Varying the…

The document describes a proposed liquidity-adjusted asset pricing analysis using monthly turnover, defined as average daily volume relative to shares outstanding. Because the measure is persistent, the author plans to model each stock's liquidity with an…

The document asks how to obtain a Green's function for zero-coupon bond pricing under the Vasicek short-rate model. It gives a pricing partial differential equation with a market price of risk adjustment and compares it with the forward Fokker–Planck and…

The document uses repeated independent fair coin tosses, with each outcome adding or subtracting one unit, to illustrate a martingale test. Its answer applies the conditional expectation definition: express the next process value as the current value times a…

The document presents a portfolio measurement problem involving two funds with different valuation schedules and cash-flow rules. One fund is valued monthly, allows cash flows only at month-end, and can use time-weighted returns. The other is valued…

The document derives the dynamics of a short-rate process whose definition includes both a deterministic time integral and an Itô integral. The key step is to name the stochastic integral as a process, then express the rate as a function of time and that…

The document examines a backward adjustment factor used to account for cash dividends in historical equity prices. It asks whether multiplying pre-ex-date prices by a factor based on the dividend and the price immediately before the ex-date preserves total…

The document explains why a trader who steps ahead of a large displayed buy order may have value even when a rising market leaves the trader unfilled. It separates the upward-price scenario into three cases: the order fills before prices rise, fills only…

The document raises a methodology question about selecting near- and next-term options when calculating intraday CBOE VIX values under the post-2014 maturity rules. It describes the eligible terms as more than 23 and fewer than 37 days to expiration. As time…

The document asks whether portfolio plots built from combinations of several stocks are plausible and why they show few portfolios with both low returns and high standard deviation. The portfolios use weekly return and volatility estimates, with the asset…

The document considers a Kolmogorov–Smirnov test applied to returns from simulated geometric Brownian motion. The question describes simulating many terminal asset prices, converting them to returns, fitting distribution parameters, and testing the returns…

The document explains how to convert an annually compounded interest rate into the continuously compounded rate used in the Black–Scholes model. Equating the accumulated value under each convention over the same time horizon gives the conversion: take the…

The document explains two ways to express a return over multiple years as an annual figure. With annualized linear returns, the total return over the period is divided by the number of years. With compound annual growth rate (CAGR), the annual rate is the…

This exchange challenges the claim that a Constant Maturity Swap keeps a company’s debt duration near the tenor of its CMS index throughout the life of the trade. CMS names the rate used to reset a leg, such as the prevailing five-year swap rate; it does not…

This discussion examines the commonly used SABR at-the-money volatility approximation that keeps only the leading term, alpha divided by the forward price raised to one minus beta. The fuller Hagan expression includes correction terms involving expiry, the…

This exchange explains how to bootstrap an EONIA curve in QuantLib-Python with a reference date that stays fixed when the evaluation date changes. The proposed solution is to use the `PiecewiseLogCubicDiscount` constructor that accepts an explicit reference…

The document asks how to compare two models that produce probability distributions for future returns. One proposed method is to add the probabilities assigned to observed outcomes, but the response instead evaluates the joint likelihood of the realized…