Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
10,263 documents
The explanation links sticky-delta implied volatility to scale invariance in asset-price models. If scaling the initial spot and strike by the same factor scales a European option’s value by that factor, the option price is homogeneous of degree one.…
The document addresses whether a general-purpose quantitative finance library can value swaps whose cash flows depend on equity or index performance. Its answer is that the core library does not provide the needed instruments directly. For users working in…
The document addresses fair value when a futures contract is settled in one currency while its underlying spot price and dividends are quoted in another. Its central principle is to express the cash flows in a consistent currency and use the appropriate…
The discussion examines whether an option’s quoted price captures the cost of hedging when implied volatility varies across the life of the trade. In an illustrative case, volatility is expected to be concentrated in one part of the option’s life. The answer…
The question describes a two-factor Hull–White short-rate model in which the short rate combines a deterministic shift, calibrated to the initial forward curve, with two mean-reverting Gaussian factors. It asks how to update the entire forward curve through…
The discussion distinguishes modeling returns under the real-world probability measure for risk analysis or portfolio construction from modeling under the risk-neutral measure for derivatives pricing. For observed log returns, estimate the mean and variance…
The discussion explains why swap desks may maintain several interest rate curves. In a multicurve framework, an overnight indexed curve is used to discount future cash flows, while separate curves estimate the future fixings that determine floating-leg…
The document considers how to form a self-financing portfolio of bonds and stocks to replicate a basket of options, with each option written on a different underlying stock. It suggests constructing a replicating portfolio for each option separately and then…
The document asks whether a stochastic volatility model and its Gyöngy local volatility counterpart imply equal option prices and hedging costs. It describes the relationship as matching the terminal distribution of the underlying under the two processes,…
The document compares Heston stochastic volatility with Vanna–Volga (VV), an interpolation approach used to construct an FX implied volatility smile. It describes VV as requiring a small set of market volatility quotes, commonly at-the-money and 25-delta…
The note concerns constructing an FX volatility surface when market quotes are expressed by moneyness or delta rather than by fixed absolute strikes. It describes limitations encountered with Python bindings for QuantLib and an Open Source Risk Engine…
The note explains why option models are often calibrated directly under a risk-neutral measure using observed option prices, without first specifying a corresponding physical-measure process. The calibrated model is used to extrapolate prices beyond the…
The document considers a one-period security with finitely many possible terminal prices, all above a call’s strike. Since the call is certain to finish in the money, its payoff in every state equals the security price minus the strike. This makes the call…
The document asks whether a discretely sampled arithmetic Asian option depends on forward implied volatility. It compares the question with forward-starting and barrier options, whose values can be sensitive to the volatility smile at a future reset date,…
The document raises an interview question about how a digital, or binary, option is priced when the spot price is modeled with a normal distribution versus a lognormal distribution. It suggests that the lognormal model’s heavier right tail might make the…
The document explains why an option’s time value is generally greatest near the money and declines as the option moves deep in or out of the money. It uses delta hedging for intuition: a long option hedged with the underlying can earn from rebalancing as the…
The document addresses a one-factor Hull–White calibration that fits mean reversion and a single volatility parameter to market normal-volatility quotes for at-the-money swaptions. The reported fit is poor across quotes, raising the question of how to…
The document explains how an issuer’s call right is incorporated when valuing a callable bond on a binomial interest-rate tree. Valuation proceeds backward from later dates: at each node, the model discounts the possible next-period bond values using the…
The document explains the role of the vector parameter that maps a multidimensional affine state process to the scalar quantity in an option payoff. In the stated call-pricing expression, the payoff depends on an exponential of that projection, and the…
The discussion asks whether Heston option prices have a convenient approximate Black–Scholes implied volatility formula, comparable to formulas used with other stochastic volatility models. Heston European option prices can be computed accurately through…
The document explains why a futures contract can have zero value while its quoted futures price changes. Daily mark-to-market settlement credits or debits the trader’s margin account, resetting the contract’s value while transferring each price change as…
The document addresses how to estimate implied volatility for expiries shorter than the first available maturity on a volatility surface, with very short dated binary options as the motivating use case. One proposed method is to hold volatility flat at the…
The document presents ways to validate option pricing and Greek calculations across analytical, finite difference, binomial, and Monte Carlo methods. For models with closed form solutions, it recommends comparing against formulas and worked examples, while…
The document considers a payoff that pays the positive amount by which one correlated lognormal stock exceeds a strike, provided a second stock finishes between two bounds. It starts from the discounted expectation and explains how to split the payoff into a…