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The document presents a finite-state price tree for an underlying asset, with zero interest and a cash dividend paid between observation dates. It sketches how to find risk-neutral transition probabilities by matching each node’s current value to the…
The document explains why delta hedging an at-the-money option close to expiration can leave a trader exposed to uncertainty over exercise. If a short option is exercised, the seller may end up with a risky position in the underlying; if the hedge was placed…
The discussion considers why Monte Carlo estimates of a call price under the SABR stochastic volatility model may disagree with prices obtained using the commonly cited SABR implied volatility formula. One answer points to discretization bias: a basic Euler…
The document frames an optimization problem: selecting asset allocations across successive decades over a century, using a restricted set of choices among equities, cash, and bonds. Each period permits either a full allocation to one asset or an equal split…
The document explains why par instruments are commonly used to represent a yield curve and how a par curve relates to zero-coupon and forward curves. A zero curve, obtained through bootstrapping, represents discount rates for individual future cash flows.…
The document examines proposed ways to adjust option vega for time to expiry and asks whether such adjustments can be justified by dividing vega by the square root of time. It explains that ordinary vega is already a meaningful sensitivity for a particular…
The document distinguishes an option’s implied volatility (IV) from its vega. IV is an input to an option pricing model, while vega measures how much the modeled option price changes when IV changes. A larger vega for one option therefore does not show that…
The document derives the return on a stock position financed partly with investor cash and partly with a loan. Starting from the stock’s terminal value as its initial price multiplied by one plus its return, it subtracts the investor’s initial contribution…
The document raises the practical problem of calibrating local-stochastic volatility models when an FX volatility surface has only a few quoted strikes per maturity. It notes that standard FX quotes may be expressed through at-the-money straddles and…
The document discusses how to convert a foreign-currency trading gain or loss into a home currency, using a USD/JPY trade as its example. It reports a loss measured in yen and explains that conversion into dollars uses the rate applicable to selling dollars…
The document derives the solution to an SDE in which an asset’s drift and volatility are deterministic functions of time. Applying Itô’s lemma to the logarithm of the asset value introduces a second derivative term. The quadratic variation of the diffusion…
The document investigates why cubic interpolation of discount factors in QuantLib might produce zero or irregular forward rates near a curve endpoint, in contrast with log-linear interpolation. It describes a curve built from dated discount factors and…
The document asks how to obtain a binary option value from the change in call prices across nearby strikes. With implied volatility held constant, the limiting price difference corresponds to the negative strike derivative of the call price, which is the…
The document asks whether the Sharpe ratio denominator should account for a time-varying risk-free rate, including its volatility and correlation with portfolio returns. The answer frames the ratio as return per unit of risk for a zero-cost position. Under…
The document asks how to build a consistent historical swaption volatility series when market conventions change. It distinguishes normal from Black volatility and quotes referencing IBOR or OIS discount curves, and asks whether backtests should use only…
The note describes using meeting-date overnight index swaps to infer market expectations for central bank rate decisions. The proposed comparison is between the current effective overnight rate and the OIS rate spanning the period around a policy meeting.…
The note clarifies what a two-year spot rate represents when valuing fixed-income cash flows. It is the rate used to discount cash flows occurring at the two-year horizon, such as the second annual coupon payment on a coupon-bearing bond. The same…
The note explains why Walt Disney Company filings may appear under two different SEC Central Index Key identifiers. The question arises from searches showing older annual reports under one identifier and a later filing under another, creating uncertainty…
The note addresses whether reinforcement learning is meaningful for trading models that assume orders do not affect order-book dynamics. Its answer is that actions need not change the state transition process: a decision process can still specify available…
The document reproduces a university course description, tentative schedule, reference books, and a long research reading list for quantitative trading. The syllabus spans statistical arbitrage, asset-return properties, statistical models, trading…
The document clarifies a common misunderstanding of the Feynman–Kac theorem in a stochastic calculus text. The theorem is not asking the reader to discover an unknown terminal function: the payoff function is specified as part of the problem. A derivative’s…
The document distinguishes instantaneous, risk-free arbitrage after transaction costs from trades that require holding inventory while prices may converge. In a proposed cross-exchange trade involving a stock and cash, the question is how to hedge the stock…
The document addresses which options to use for research on S&P 500 index options, comparing contracts on the index, its futures, and exchange-traded funds. It offers a concise liquidity assessment based on electronic-market bid-ask spreads measured in…
The document clarifies the distinction between deterministic and random simple processes in stochastic calculus. A deterministic process has values that are known in advance, while a random process has values that depend on uncertain future outcomes. This…