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20,364 dokumenter
The document explains why a stock used as numeraire changes the stock’s drift under the associated pricing measure. In a Black–Scholes setting with constant volatility, the drift becomes the risk-free rate plus the variance rate. The central idea is that…
The document outlines three limitations of Brownian motion as a model for financial prices. Its continuous paths cannot represent sudden price jumps, and its Gaussian assumptions may fail to capture the distribution of market returns. It also raises…
The document addresses which book equity measure to use when replicating a monthly book-to-market variable in a study of expected stock returns. The accepted response infers that the intended numerator is common equity, even though the paper does not…
The document defines a complete market as one in which every derivative payoff can be replicated using positions in the traded securities. Replication makes it possible, in principle, to hedge away the uncertainty in a derivative by trading those securities.…
The document explains why an American digital put can be valued through the probability that the underlying asset reaches a specified minimum by expiry. The key reasoning is about exercise timing: when interest rates are nonnegative, the response says it is…
The document considers whether a practical option model can produce better delta hedges than Black–Scholes for equity options. One response says the Heston model is relatively quick to implement analytically, but may still miss important features of…
The document describes a CPI forecasting regression whose author sees a moving average of the residuals moving in the same direction as CPI. The author asks whether this suggests omitted-variable bias, biased coefficients, or another modeling problem. The…
The document presents competing views on calculating a strategy’s Sharpe ratio when it has no open positions. Some responses argue for excluding such days because they have no realized strategy return and including zero or forward-filled observations could…
The document compares three ways of working with investment factors. One approach builds long-short portfolios by ranking stocks on a characteristic such as price-to-book and buying the highest-ranked group while shorting the lowest. The author notes that…
The document raises a question about a statement in a paper on variance swaps: a stock call option’s vega is greatest when the option is at the money. The author wonders whether this is because vanilla options are nearly linear in volatility at that point,…
The document asks how to automate daily retrieval of CDOR rates, swap rates, and options prices from Bloomberg into an Excel workflow. The answer recommends sending requests through Bloomberg's WAPI, which it says refreshes data when a request is sent,…
The document asks what interpolation method is suitable when perturbing a key interest rate to estimate the sensitivity of a portfolio’s value. The question contrasts a book’s use of linear interpolation with the concern that a linear curve may be…
The document asks why the present value of the tax shield from constant, perpetual debt is expressed as the corporate tax rate times interest payment divided by the expected return on debt. The response characterizes the expected return as the discount rate…
The document discusses the cross-variation of two Brownian motions and the role of their dependence. For independent Brownian motions, their increments have zero covariance, leading to zero cross-variation. For correlated motions, the answer represents one…
The document asks whether an option on a bond future can be represented using options on forward rates. It simplifies the contract to a European option on a zero-coupon cheapest-to-deliver bond and relates the forward bond price to the forward rate over the…
The discussion investigates why Yahoo Finance showed a daily trading-volume figure that did not match the sum of its hourly figures for a Japanese-listed stock. The explanation is that the daily number represented volume on the primary exchange, while the…
The discussion explains that changing probability measure can change the distribution of a counting process, including its Poisson intensity. An equivalent measure need not preserve the original Poisson law: one example tilts probabilities toward a…
The discussion asks whether a five-year zero-coupon yield can be derived from one-, two-, and three-year zero-coupon rates when longer maturities are unknown. Its central lesson is that the available spot rates do not determine the five-year rate on their…
The discussion explains why a simulated delta hedge may retain tracking error and how to account for changing positions. In the Black–Scholes framework, hedge error should shrink as rehedging intervals become smaller when the simulated underlying follows the…
The document asks whether a Vasicek short rate can be set equal at the initial time to the short rate implied by a Nelson–Siegel curve. In the stated Nelson–Siegel specification, the initial short rate is the sum of the first two curve parameters, since the…
The document explains why a volatility-squared correction appears when expressing a stock price as an exponential Brownian process in the Black–Scholes framework. Under the risk-neutral measure, the discounted stock is modeled as a martingale. The answer…
The document challenges a claim that a high-frequency trading bot can detect a large cryptocurrency order, infer its hidden maximum price, buy available coins first, and resell them at that limit. The answers explain that a marketable order generally…
The document derives the dynamics of a ratio formed from a deterministic money account, a stochastic exchange rate, and a stochastic stock price. The stock and exchange rate are driven by the same Brownian motion, so their quadratic covariation contributes…
The document explains that a valuation discount rate must match the cash flow being valued. It distinguishes dividends and free cash flow to equity, typically discounted at the required equity return estimated with CAPM or another equity model, from free…