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.
8,116 documents
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 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 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 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 outlines a framework for choosing how often to rebalance a delta hedge during gamma scalping. Under geometric Brownian motion, it approximates the hedge adjustment as gamma times the underlying price move, then estimates trading costs by…
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…
The document addresses how to adjust an implied-volatility surface when its quoted option prices contain small butterfly arbitrage violations. The specific issue is a discrete set of call prices across strikes that fails convexity, which can undermine later…
The document compares non-callable bank certificates of deposit with brokered CDs, focusing on the bank CD holder’s ability to withdraw early at par while paying an early withdrawal penalty. It models that feature as an American-style put embedded in a…
The document is a brief request for an introductory explanation of the constant elasticity of variance (CEV) model, including its dynamics, strengths and weaknesses, applications to payoff types or hybrid models, and calibration. The response does not…
The document asks how to interpret the Longstaff–Schwartz least-squares Monte Carlo method for pricing American options, especially how its regression target relates to the backward recursion described by Tsitsiklis and Van Roy. The central distinction is…
The document examines how often to rebalance a delta hedge for a European call under Black–Scholes assumptions and geometric Brownian motion. The questioner estimates the local hedging error from the option’s gamma and the squared price move, while…
The document asks how to price an American-style Asian option whose exercise payoff uses the average underlying price over a recent rolling window. It explains why early exercise and path dependence complicate standard approaches: Monte Carlo and tree…
Option open-interest figures published by financial websites are generally daily snapshots, which limits their direct use in intraday analysis. The post raises the question of whether intraday estimates or suitable vendor data are available, motivated by the…
For European call and put options in a model that includes a continuous dividend yield, the zero-dividend case can be obtained by setting the yield parameter to zero. The response also points to a separate list of formulas, though it does not reproduce those…