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The document explains how to simulate terminal prices for several assets whose returns are correlated, in order to value a multi-asset option by Monte Carlo. In a geometric Brownian motion model, dependence is specified through correlations among Brownian…
The document describes a backward path-integral scheme for pricing an American put on a log-price grid. At each time step, it discounts and integrates the next-step option value against a Gaussian propagator for log prices, then applies the early-exercise…
The document derives an alternate form for the time integral of Brownian motion, a step that arises in the short-rate Merton model. Representing Brownian motion at each time as the accumulation of its increments turns the time integral into an integral over…
The document frames a model-selection problem for reinforcement-learning-based dynamic hedging of long-dated swaptions. The proposed application uses 2y2y and 4y2y swaptions, requiring simulated paths that update both a forward swap curve and an implied…
The document shows how to rewrite a European put’s discounted expected payoff as an integral of the underlying asset’s cumulative distribution function. Starting from the payoff integral over nonnegative asset prices, it extends the density’s support to the…
The document frames a research question about abrupt changes in index option prices near major expiration dates. It proposes systematic rebalancing by structured products as a possible source of price pressure and asks what other forces might contribute. The…
The document explains why a European put’s Black–Scholes–Merton value can fall below its immediate exercise payoff. A European option cannot be exercised before expiration, so when the underlying price is far below the strike, the eventual payoff is…
The document outlines a property-based method for estimating a REIT’s equity value per share. First calculate net operating income from revenue and expenses before depreciation and interest. Divide that NOI by an assumed capitalization rate to estimate the…
The document considers a weather-linked call whose daily payout depends on maximum temperature mapping to a quantity and a price index average exceeding a strike. The payoff also has daily and contract-wide payout limits, making a direct closed-form…
The document outlines a derivation of the Black–Scholes equation from the Capital Asset Pricing Model rather than from a risk-free portfolio formed by delta hedging. It starts from CAPM’s relation between expected return and covariance-based risk…
The document discusses how to interpret a LIBOR Market Model matrix when constructing discount bond values. It emphasizes that matrix layout must be understood first: under a common convention, columns represent observation times and diagonal entries…
The document examines an option whose payoff and premium are expressed in the underlying asset, using an ETH example to compare conversion from a conventional Black–Scholes value with a direct simulation. The key issue is the payoff definition: converting…
The discussion asks whether a spread move reported for a bond segment can estimate the price change of a bond trading far below par when no bond-specific price history is available. It distinguishes ordinary discounted bonds from distressed debt and explains…
The document asks how to interpret common sell-side analyst ratings on a five-point scale in quantitative terms. It uses a score associated with market-average performance as an example and asks whether ratings above that level correspond to defined ranges…
The document raises an econometric modeling question involving a GARCH(1,1) volatility equation and a fourth equation in a simultaneous system. A variable from the fourth equation enters the GARCH specification as an exogenous regressor, while the…
The document sets out a continuous-time optimal execution model for selling a fixed stock position over a chosen horizon. It assumes an arithmetic Brownian unaffected price and a linear temporary impact cost proportional to trading rate. Under these…
The document examines why the differential of a log price is not the same as the proportional price change for an Itô process, even though their squared differentials agree in quadratic-variation calculations. It applies Itô’s lemma to a price with drift and…
The document outlines possible approaches to hedging municipal bond portfolios with BMA or SIFMA-indexed swaps. For portfolios made mainly of senior variable-rate demand obligations or similar floaters, it suggests comparing the historical root-mean-square…
The document collects suggestions for obtaining historical index membership and constituent prices at monthly intervals. It points to professional data terminals and services, including Bloomberg, where index members can be queried with a date override and…
The document describes why a digital option’s stock hedge changes sharply as the underlying approaches and passes its strike. A digital option pays a fixed amount when it finishes in the money and nothing otherwise, so its payoff does not rise gradually with…
The document explains how to estimate coefficients in a regression whose intercept and slope depend on a binary state indicator. The proposed method splits observations according to the indicator’s lagged value and fits the same regression separately to each…
The document considers how to build a fundamental scoring model for a defined stock universe using metrics for size, growth, valuation, quality, and risk. It describes the practical challenge of collecting current, historical, and estimated Bloomberg fields,…
Energy retailers that promise customers fixed prices while buying power or gas at floating wholesale prices face a mismatch between sales revenue and procurement cost. The risk can grow when demand and prices move together, as during cold weather. The…
The document outlines ways to begin building a machine learning credit scoring model for a thesis, focusing on public datasets, example competitions, and learning materials. It points to credit default prediction tasks as sources of data and published…