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 surveys ways to simulate Lévy processes with infinitely many jumps, including CGMY and Meixner models. One approach uses the characteristic function to recover a distribution for inverse-transform sampling. Other methods exploit representations…
Normal and shifted lognormal volatility quotes can represent the same current swaption or cap/floor price. The document explains why this price agreement does not make the models’ Greeks agree: Greeks describe how prices change as market inputs move, and the…
The document compares two ways to derive a claim’s price in a binomial market. Backward induction explicitly constructs a replicating hedge at each step and uses the absence of arbitrage to identify the price. A second presentation introduces self-financing…
The document raises a market-convention question about quoting delta and term pairs on FX volatility surfaces for EUR/PLN and EUR/USD. It suggests that EUR/PLN may use forward delta throughout, while EUR/USD may use spot delta through one year and forward…
The document analyzes how a European in-the-money call's Black–Scholes delta changes when time to expiration increases. Delta is the standard normal cumulative probability evaluated at d1, so its sensitivity to time depends on how d1 changes, not simply on…
The document explains how to express a Black–Scholes-style lognormal price distribution using SciPy’s lognormal parameterization. If a price variable is the exponential of a normally distributed variable, the normal variable’s standard deviation corresponds…
The document considers a short call hedged with stock. As the underlying price changes, the option’s delta changes because an option’s value is nonlinear in the stock price. A stock position sized to offset delta at the initial price therefore may no longer…
The document explains how a call option can be replicated in a one-period, two-state stock model. A portfolio holding a suitable number of shares and borrowing or lending cash is chosen to match the call’s payoff in both the up and down states. Its initial…
The discussion distinguishes variance from volatility, understood here as standard deviation, and asks how a variance measure can reflect implied volatility across option strikes. One answer focuses on statistical estimation: variance is a parameter of a…
The document asks whether adding the individual option P&Ls in a foreign exchange options book gives the portfolio value. Its brief answer says yes and notes that foreign exchange markets can move around the clock, making ongoing exposure monitoring…
The document considers a leveraged turbo certificate whose value depends on the underlying price and a financing level. The financing level grows over time with daily interest, while a barrier level triggers a total loss if reached. The question asks whether…
The document explains a calendar arbitrage in a simplified setting: European calls on a non-dividend-paying stock with zero interest rates. If the shorter-dated call costs more than a longer-dated call at the same strike, the proposed trade is to sell the…
The document examines whether a swaption’s theta can be estimated from gamma and implied volatility, and why a model’s reported theta may differ from that estimate. Under the normal model, the response identifies theta as approximately negative one half of…
The document separates the effect of correlation on an individual caplet from correlation among forward rates along the yield curve. A caplet pays based on one forward rate at its expiry. Since its payoff depends on that rate alone, correlation with other…
The document discusses a proposed options spread that sells deep out-of-the-money puts and buys puts closer to the money to investigate whether far out-of-the-money puts carry a crash risk premium. The response characterizes the short-put exposure as selling…
The note concerns reproducing an implied volatility surface for foreign exchange options, with the intention of using it to calculate local volatility. The questioner suspects that strike discrepancies may stem from the forward exchange rate calculation or…
The note explains how a stock option pricing routine can be adapted to price an option on a futures contract. Its approach converts the observed futures price into a discounted pseudo spot price using the relationship between futures, interest rates, and any…
The document examines a step in Black–Scholes reasoning: delta hedging removes the diffusion term from a portfolio’s dynamics, leaving an integral over time of terms involving derivatives of the option value and the underlying price. It asks why this…
The document describes a European call whose exercise condition depends only on one commodity futures contract, while exercise also grants the holder a second futures contract. The payoff is the usual positive excess of the first asset over the strike, plus…
The document asks how to pair a large underlying price shock with plausible implied volatility changes when stress testing an options portfolio. It compares three approaches: applying a uniform volatility increase, using a high historical volatility level,…
The document examines raw moments of a straddle payoff at expiry and asks whether the call and put components can be treated as independent. For a call payoff C and put payoff P at the same strike and maturity, the accepted explanation notes that both cannot…
The document asks how to interpret a claim that single-factor interest-rate models can make the vanilla-option hedge for a Bermudan option sensitive to changes in the yield curve. The author observes that hedges in any model may need rebalancing when rates…
The document considers calibrating Hull-White and Jarrow-Yildirim interest rate models when only nominal and inflation-indexed bond prices are available. It clarifies that in the Hull-White bond formula, time zero represents a bond starting now, the…
The document examines a common misunderstanding in Black-Scholes: with spot equal to strike and a zero interest rate, the exercise probability is not generally one half. Under the model, the probability of finishing in the money is represented by the…