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The document explains how the choice of probability measure in interest-rate pricing follows from the chosen numéraire. Under the measure associated with a traded numéraire, asset prices expressed relative to it are martingales. This gives a practical way to…
The document examines an apparent mean-reverting basket built from several foreign-exchange rates. The proposed process fits a linear regression to estimate hedge ratios, forms a spread, then applies an augmented Dickey–Fuller test. The reported significance…
The document poses a valuation problem for a forward-starting interest-rate swap in a binomial short-rate lattice. The swap begins after the valuation date, receives floating payments, pays a fixed rate, and makes payments in arrears. The questioner reports…
The document asks for a rigorous interpretation of the functional derivative terms in Bergomi’s pricing equation for a European claim. The price is viewed as depending on spot and a family of stochastic processes indexed by future times, which raises…
The document derives a zero-coupon bond price when the short rate starts at a fixed level and rises by a fixed increment at each jump of a Poisson process. The discount factor depends on the time integral of the jump count. By exchanging the order of…
The document discusses whether to include an intercept when estimating the hedge ratio for a pairs trade. For two integrated asset price series that are cointegrated, it presents a regression with a slope and constant, where the residual is stationary.…
The document explains why a binary call and a standard European call with matching contract inputs do not have the same delta. A vanilla call has a payoff that rises continuously with the underlying above its strike, while a cash-or-nothing binary pays a…
The document collects learning resources for someone starting with volatility modeling, especially local volatility and surface calibration. It points to a practitioner book and lectures, a thesis focused on calibrating a local volatility surface, and a…
The document considers whether varying the autocall level of an autocallable bond can reproduce the value of an issuer-callable bond priced with an optimal exercise policy. It explains that the issuer-callable bond is no more valuable than an autocallable…
The document explains why QuantLib’s swap rate helper divides the target net present value by the fixed-leg BPS, then scales by a basis point. The fixed-leg BPS measures how much the fixed leg’s value changes when its coupon rate moves by one basis point.…
The document explains the leverage effect by separating a company’s enterprise value from its financing. In a simple example, a business owns a gold asset and has fixed nominal debt. As the asset value changes, the debt claim stays fixed while the residual…
The document derives the conditional expectation of the time integral of a standard Brownian motion over an interval, given the information available at the interval’s start. The result is the interval length multiplied by the Brownian value at that start.…
The document raises a terminology question about liquidity rebates: whether they go to any trader placing a limit order or specifically to a market maker. It contrasts a general description of limit-order traders as liquidity providers with readings that…
The document explains how trading in S&P 500 futures can be connected to movements in the cash index, even though a futures trade does not directly sell shares in the index constituents. Futures are marked to market daily and ultimately settled against the…
The document explores why option-pricing ideas have not become a routine way to value risky corporate cash flows. It presents the structural analogy in which equity resembles a call option on firm assets and debt resembles a liability exposed to the firm's…
The document compares two ways to price a callable zero-coupon bond in the Ho-Lee short-rate model. One method values the bond as a straight zero-coupon bond minus a European call on that bond. The other represents the callable bond as a claim whose value…
The document poses a modeling question about pricing European options with dynamic programming. The proposed setup treats option hedging as a discrete-time, continuous-state Markov decision problem and uses a risk-sensitive action-value function: instead of…
The document gives a brief hint for a quantitative finance exercise about a European call option’s value as a function of its strike. It writes the price as an integral of the option payoff over a distribution of the underlying value, then relates…
The document describes a cross-sectional method for decomposing stock returns into world, country, and industry components. Monthly weighted least squares regressions relate individual stock returns to country and sector indicators, using market…
The document explains why cumulative return charts can show gaps when asset return series contain missing observations. Those gaps reflect the data and should not be hidden by chart-level interpolation, since filling values changes the underlying return…
The document is a categorized directory of online sources for finding quantitative finance research and related publications. It covers platforms that let readers search, view, or download papers; indexing services that can help locate open versions; a…
The document discusses how to reduce the risk of trading spurious cointegration by screening candidate assets for economic relationships. It recommends looking for securities with strong ties, such as related commodity benchmarks, a commodity and associated…
The document clarifies a proposed volatility adjusted moving average crossover for fixed income momentum. A shorter moving average of an index represents a more recent price level, while a longer moving average represents a smoothed longer term level. Their…
The document explains how to extend a Heston stochastic volatility option model with jumps in the underlying asset. It recommends first considering a jump diffusion such as Merton’s model, which uses lognormally distributed jump sizes, or Kou’s model, which…