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The document asks how to derive an approximation that maps at-the-money implied volatility to volatility at another strike under a lognormal distribution. The relationship is framed as a strike-dependent scaling rule, using the ratio of the at-the-money…
The document asks why two stated formulas for option vanna appear to differ by a factor of one hundred. It gives expressions involving spot price, volatility, time to maturity, the Black-Scholes variables, and vega, then reports that substituting a…
The document questions whether a bank’s coded option pricing function can sensibly be used to calculate the profit and loss of a short option position. It presents a one-period P&L expression that combines the change in the option’s model price, interest on…
The document explains that an incomplete market generally has multiple equivalent martingale measures rather than a unique risk-neutral measure. For a nonreplicable claim, expected discounted payoffs under these measures yield a range of arbitrage-free…
The document clarifies that “heat-map method” may refer to a way of assessing VaR model performance rather than a procedure for calculating VaR. In the answer provided, historical VaR breaches are counted over a review window and mapped to colored zones: a…
The document explains why investors searching SEC filings may not find loan-level ABS-EE data for residential mortgage-backed securities. The key distinction is between publicly registered offerings, for which loan-level disclosures are required, and Rule…
The document explains how counterparties manage exposure on OTC variance swaps when initial or maintenance margin is not posted. It says that many OTC swaps are governed by a credit support annex, but arrangements vary; without margin, counterparties rely…
The document challenges the idea that PCA and machine learning are rarely used in trading. It notes that machine learning covers many methods, from linear regression to random forests, and that firms have had varying degrees of success with them. It then…
The document considers how a leveraged exchange-traded fund affects the Sharpe ratio. Its answer applies a simple proportional scaling argument: if returns are doubled, their expected value doubles and their variance quadruples, so their standard deviation…
The document explains why an uncollateralized OTC derivative can still impose funding costs on a bank, even though the trade itself requires no initial cash. One source is the hedge: the bank may hedge through collateralized interbank trades, and adverse…
The explanation frames interest-rate hedging as offsetting the sensitivity of a portfolio’s market value to movements in the risk-free curve. It values a debt instrument by discounting its dated cash flows using factors that reflect rates and other…
The document asks how to calculate the remaining principal on a loan when interest accrues using Actual/360 or Actual/Actual day-count conventions. It contrasts these methods with a 30/360 amortization, for which a level-payment annuity formula can express…
The discussion diagnoses an implausibly large cumulative return in a simple moving-average crossover backtest. The strategy uses closing prices and a 10-day simple moving average to set a long or short position, then applies that position to daily asset…
The discussion examines whether corporate bond OAS should be adjusted for price or coupon differences when comparing bonds from the same issuer. It distinguishes a bond’s long-term value relative to a credit curve from its short-term trading value, which may…
The document addresses why nearby option strikes can show sharply different open interest. Its proposed explanation is a preference for round-number strikes: traders may concentrate positions at salient levels such as 7,400, leaving a nearby strike like…
The note explains why the effect of implied volatility on a vertical credit spread depends on the net Greeks of its two option legs. A credit spread sells one option and buys another with the same expiration but a different strike, receiving a net premium at…
The document considers why a stock price can move repeatedly even when company news does not arrive at the same pace. It presents price as a noisy proxy for underlying value: after news, market participants may take time to interpret its implications and…
The note distinguishes quoted bond prices from bond yields. It explains that a U.S. bond price such as 99 1/8 represents 99.125 per 100 of par, while a yield is the discount rate that equates the present value of coupon and principal cash flows with the…
The document compares two ways to forecast daily variance with a GARCH(1,1) model when five-minute returns are available. In the first approach, the model is fit or applied at the daily horizon, using a realized-variance estimate and a prior daily variance…
The document discusses the purpose of meta-labeling in machine-learning trading systems. It responds to the concern that a secondary model merely filters trades and might overfit historical examples. The proposed framing is to start with a primary strategy…
The document poses a terminal-value PDE in two variables with second derivatives in each variable, a mixed derivative, and a source term proportional to one state variable. It asks how to solve the equation when reducing the two-dimensional dependence…
The document explains how to simulate a geometric Brownian motion after changing from the physical measure, where the drift is the expected return, to the risk-neutral measure, where the drift is the risk-free rate. It derives the change in Brownian motion…
The document considers how to simulate correlated asset returns for Monte Carlo mean-variance portfolio optimization. A common approach starts with independent standardized draws and multiplies them by a matrix factor of the target covariance matrix,…
The document distinguishes utility representations under certainty from expected utility under uncertainty. Under certainty, any increasing transformation of a utility function preserves the ranking of preferences. With lotteries, preferences are represented…