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The document asks for the transition distributions of two continuous-time processes: Brownian motion with constant drift and an Ornstein–Uhlenbeck process that reverts toward a long-run mean. Its answer derives the Ornstein–Uhlenbeck solution from an initial…
The document concerns taking a Bachelier call option’s partial derivative with respect to strike and finding a mismatch between two reference results. The resolution is that the sources use different stochastic differential equations: one includes a drift…
The document discusses how to answer a broad interview question about forecasting a stock’s future behavior. It distinguishes estimating returns from measuring risk, mentioning historical mean returns, volatility, market sensitivity, and risk-adjusted…
The document introduces the Campbell–Shiller regression as a way to test the expectations hypothesis of interest rates. It describes comparing a yield spread with a subsequent change in yields, while noting that empirical estimates may differ from the…
The document raises a risk-measurement question about calculating DV01 for a USD–KRW cross-currency swap. It describes building a USD discount curve so observable USD interest-rate swaps have zero present value, and a KRW curve so observable cross-currency…
The document responds to a broad request for a practical starting point for forecasting European government or other bond prices from historical data. Its central modeling recommendation is to forecast bond returns rather than prices directly. It then…
The document asks how portfolio volatility reports might better match investors’ perception of risk. It starts from the sample standard deviation of monthly returns and notes that the estimate depends on the length of the lookback window. The questioner…
The document explains the par-yield curve as a plot of bond yields to maturity against their terms to maturity. A par yield is the coupon rate that would make a bond’s price equal to par; for a bond priced at par, its coupon rate and yield to maturity…
The document examines a gap option with a trigger level that differs from the strike. Its payoff is zero below the trigger and equals the underlying price minus the strike above it. When the underlying finishes above the trigger but below the strike, that…
The document asks how to rigorously establish the Markov property for the Heston model’s joint stock-price and variance process, whose square-root variance dynamics do not meet the familiar Lipschitz conditions cited in many introductory SDE results. It…
The document discusses how a student on a limited budget might obtain historical trade-by-trade prices and sizes for NYSE and Nasdaq stocks. The question distinguishes exchange-wide coverage from data limited to trades executed on a single venue, and notes…
The document asks whether predicting an option’s delta more accurately than Black–Scholes can create trading opportunities beyond improving a hedge. It frames the question with an example in which a model estimates delta at 0.4 while Black–Scholes gives 0.3,…
The document introduces a state price vector through a two-state example: inflation is either above or below a threshold, and a security pays in one state but not the other. It describes the collection of state-contingent prices as a vector, and says…
The document explains how incoming buy orders can alter the best bid and ask in a limit order book. A buy priced below the best bid leaves the displayed best bid unchanged; one at that price adds quantity; and a more aggressive buy can establish a new best…
The document raises a replication question about Ledoit and Wolf’s covariance matrix shrinkage method. The author is trying to reproduce a plot relating Percentage Relative Improvement in Average Loss (PRIAL) to the ratio of the number of variables to the…
The document compares absolute changes in interest rates with percentage changes when constructing historical return series for value-at-risk analysis. Its example shows how an identical change in yield can produce very different percentage returns depending…
The document explains a buy-sell-back as a collateralized loan structured through a security sale followed by a forward agreement to sell the security back. The borrower receives cash against a bond or other security, while the lender holds the collateral…
The document considers a statistical-arbitrage workflow that applies principal component analysis to stock log returns, regresses each stock’s returns on leading components, and models the resulting residuals for mean reversion. The researcher tries to fit…
The document examines whether a stock-liquidity regression should include yesterday’s liquidity when its residuals appear serially correlated. The setting is German stocks modeled with price, free float, and book-to-market variables, alongside time fixed…
The document frames a thesis question about established, pre-neural-network approaches to calibrating stochastic volatility models, with particular interest in Heston. It asks for research areas and papers that could support a historical overview of…
The document examines a small mismatch between a GBP overnight index swap market quote and a displayed zero rate. It calculates a one-week discount factor from the quoted rate using a simple day-count fraction, then converts that factor to a continuously…
The document presents a market-neutral portfolio optimization objective that minimizes the absolute sample correlation between portfolio log returns and an index’s log returns. Long and short security weights determine portfolio value at each time, from…
The document asks how to derive a three-month forward rate from short-rate paths simulated under the one-factor Hull–White model, with monthly time steps. It proposes using the model’s zero-coupon bond formula to obtain discount factors over monthly…
The document examines a derivation that applies Itô’s formula to the discounted payoff of a call option inside a conditional expectation. It raises questions about when differentiation can be interchanged with expectation, how the payoff derivative enters…