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The document describes a calibration question for the eSSVI implied volatility surface, where parameters are fitted slice by slice across maturities. It focuses on a calendar-consistency inequality that links the current slice parameters to those of the…
The document explores when early exercise can be optimal for American put options in zero or negative interest rate settings. It contrasts the familiar positive-rate intuition for calls with the corresponding conditions for puts, noting that early exercise…
The document addresses how to compare portfolio performance from quarterly observations over a common sample period. It converts the cumulative return into a per-quarter compounded rate using the number of observations, then annualizes that rate by…
The document explains Euler’s theorem for differentiable homogeneous functions. If scaling every input by a positive factor scales the function by that factor raised to degree k, then the dot product of the input vector with the function’s gradient equals k…
The document derives the dynamics and solution of a linear stochastic differential equation with affine drift and diffusion by dividing the process by a carefully chosen geometric Brownian motion. Applying Itô’s product rule to the process and the reciprocal…
The document discusses how traders might estimate volatility for option analysis when the appropriate historical lookback is unclear. It describes two choices in historical volatility calculation: the length of the past period being measured and the spacing…
The document distinguishes historical volatility, calculated from past stock returns, from Black–Scholes implied volatility, inferred from traded option prices. Historical volatility summarizes observed movements, while implied volatility reflects the option…
The document raises a model-development question about choosing observation dates for behavioral credit scoring. Such models use account activity, arrears, advances, and other customer information to estimate whether an existing borrower will default during…
The document examines a proposed return model combining Fama-French factors with industry random intercepts. The modeler reports a strong relationship between residuals and fitted values and suspects that correlations among industry effects or a nearly…
The document explains that a discount curve does not need to use one universal compounding or day-count convention. For no-arbitrage pricing, the underlying discount factor for a given cash flow date is the key quantity; different conventions can express…
The document distinguishes a yield curve as a general representation of market interest rates across maturities from a swap curve as one curve built from swap market rates. It explains that other instruments, including government bonds and interbank rates,…
The document asks how inflation risk can affect corporate bond spreads, drawing on Kang and Pflueger’s distinction between inflation volatility and inflation’s relationship with real cash flows. It raises questions about why uncertain inflation can raise…
The document derives the expected terminal stock value conditional on the stock finishing above the strike, a term used in the Black–Scholes call price. It starts from geometric Brownian motion, converts the condition that the terminal price exceeds the…
The document resolves an apparent conflict between the intuition that higher coupon rates mean higher bond convexity and the claim that zero-coupon bonds have the greatest convexity. The key is the definition: convexity is the second derivative of bond price…
The document describes a Fama–MacBeth cross-sectional regression of stock excess returns on idiosyncratic volatility, log market capitalization, book-to-market, and beta. The researcher reports statistically significant coefficients and says the…
The document outlines how mortgage securitizations were modeled and divided into rated tranches. The response describes using historical mortgage default and loss data, applying stress scenarios, estimating pool cash flows and subordination, and sizing…
The document raises a backtesting problem for a systematic strategy that repeatedly buys one-year, 90% strike equity index puts and rolls them shortly before expiry. It proposes repricing the option each month with Black–Scholes using the current spot,…
The document asks whether adverse selection after a limit-order fill has a characteristic time horizon. The question describes an immediate price move against the resting order, followed by the possibility that the market later reverses. The response says…
The document asks how much a short straddle could earn in the long run under an efficient market and Black–Scholes assumptions. It assumes the implied volatility used to price options matches future realized volatility, which remains constant over the…
The document poses a stochastic differential equation driven by standard Brownian motion, with a drift proportional to the state and a diffusion coefficient that depends on its absolute value. The author asks what sense of uniqueness applies and how to find…
The document addresses whether industry portfolio returns from Kenneth French's data library can be converted into historical prices. Its answer is that the portfolios are collections of stocks and do not have a single underlying traded price series. Returns…
The document explains why a QuantLib schedule moves a swap's Saturday effective date to the following Monday. The schedule uses a business-day convention for date adjustment; the example uses Modified Following, which shifts a non-business date according to…
The document gives two ways to form a bond portfolio with matched dollar BPV, making the portfolio duration-neutral while retaining positive convexity. One example pairs a lower-coupon Treasury with a higher-coupon Treasury of a nearby maturity. The stated…
The document presents a one-period market with three possible states and two assets: a risk-free asset and a risky asset whose returns differ by state. It asks how to prove that no arbitrage exists and how to describe the family of state price vectors when…