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 document discusses when early exercise of American calls and puts may be preferable to selling the option. For calls near a dividend date, one response compares immediate exercise with the discounted value of future exercise under a near-zero-volatility…
The document considers how to make multi-year options backtests faster when a large MySQL table becomes slow under broad filters. The answer characterizes historical market data as a write-once, read-many workload that often does not need transactional…
The document reviews conditions for a set of call prices to be consistent with a risk-neutral distribution and free of static arbitrage. It describes nonnegative call spreads and butterfly spreads, which correspond to call prices decreasing and convex in…
The document poses an arbitrage question about an American put in a binomial stock-price tree. At an intermediate node, it assumes early exercise is optimal and that every terminal descendant remains below the strike. The proposed portfolio combines one put…
The document asks how practitioners build a smooth foreign-exchange volatility smile from a small set of quoted points: at-the-money volatility, risk reversals, and strangles at two delta levels. It also asks which interpolation and extrapolation methods are…
The document considers a three-year autocallable payoff with annual observation dates. It terminates early when the underlying finishes above its initial level, paying a coupon-linked amount; otherwise, the final payment depends on whether the underlying…
The document asks whether vanilla calls and puts, across strikes and maturities, can be combined with their underlying assets to create a payoff with roughly equal chances of doubling the invested capital or losing it all. It distinguishes the desired…
The document clarifies two steps in deriving the Black-Scholes equation. In a delta-hedged portfolio, the stock price appearing in the instantaneous change is the price at the start of the infinitesimal interval. It is known at that time, even though the…
The document explains why annualizing average absolute daily returns gives a multiplier near twenty, while scaling a daily standard-deviation estimate by the square root of the number of trading days gives a multiplier near sixteen. Under normally…
The document concerns fitting an option-value model of retirement, where an individual chooses the retirement year that maximizes the value of future wage and retirement-income streams. The model includes preference and persistence parameters, and the…
The document explains how Itô’s lemma extends to an option whose value depends on time, the underlying price, and stochastic variance. With correlated Brownian drivers, the differential includes second derivatives in price and variance, plus a mixed…
The document concerns an argument connecting bounded probability forecasts, modeled as an arithmetic Brownian motion, with arbitrage restrictions on binary forecasts. The response frames a forecast bet as similar to a cash-or-nothing binary option: its…
The document explains why option traders fit a curve to implied volatilities when pricing or comparing vanilla options. Market quotes are sparse across strike, maturity, and forward level, so a fitted curve lets a trader interpolate values at points where no…
The document explains how to assess whether a position with options expiring on different dates will be profitable. Its example combines calls expiring first with a put expiring later, and defines total profit from the option payoffs at both dates less the…
The document raises a market-pricing question about VIX options on futures. It observes that one-dollar-wide vertical spreads marked at half their strike width appear to share approximately the same strike across expirations, even when VIX futures are in…
The document considers how to establish reference values when a merger is combined with spin-offs. Its example involves the creation of a merged company alongside separately listed spin-off companies. The question proposes valuing the merged company from the…
The document asks whether pricing options from a Black–Scholes volatility surface implied by calibrated Heston parameters gives the same values as direct Heston pricing. It distinguishes vanilla options, used to calibrate the model, from other payoffs such…
This discussion derives the strike at which a Black–Scholes call has delta 0.50 and clarifies why that strike need not equal the usual forward or spot-based at-the-money strike. Under the Black–Scholes call delta, the condition is that d1 equals zero.…
The document discusses a complex integral that appears in a Heston-model derivation and asks why the residue theorem can be applied to one term but not another. One answer explains that the exponential factor in the limiting term decays on a lower-half-plane…
The document relates variance swap volatility to an implied volatility smile under a pure diffusion assumption. It presents an integral expression in a transformed moneyness coordinate where the smile is weighted by a standard Gaussian distribution. In that…
The document asks how hedging can be profitable under a semi-strong efficient-market assumption. It frames hedging as taking an exposure to one source of return while offsetting another, illustrated by owning an asset driven by two factors and shorting a…
The document raises a question about gamma for a short INR/JPY put option and lists the trade’s notionals, strike, spot, maturity, volatility, and interest rates. It reports a delta of 0.56 and gamma of -2.26, then asks why gamma could exceed one or the deal…
The document examines a Bloomberg convention for setting volatility in a Hull-White short-rate model. The described calculation converts a cap volatility into a rate volatility by multiplying the quoted cap volatility by the corresponding swap rate expressed…
The document raises a practical valuation problem in an illiquid options market: wide bid-ask spreads across strikes make a single option price, implied volatility, and volatility skew difficult to estimate. It provides an example snapshot for a call and put…