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 derives an expectation involving the terminal stock price multiplied by an indicator that the stock finishes above a strike. It shows how to evaluate the risk-neutral expectation directly by integrating the lognormal stock distribution, without…
The document explains the interest rate convention used in an implied volatility approximation and how to estimate an asset’s forward price. It treats the constant interest rate as the annualized risk-free rate, assuming the rate used in the approximation…
The document derives a closed-form price for a European currency call when domestic and foreign interest rates follow Hull–White dynamics and spot FX has constant volatility. It changes from the domestic risk-neutral measure to the domestic maturity-forward…
The note explains how the transition from LIBOR to SOFR affects the optionlets included in a standard one-year USD interest-rate cap. In the LIBOR convention described, the first rate fixing is already known at the start date, so the cap begins with the…
The document asks how to break an option position’s Vega P&L into contributions from at-the-money volatility, skew, curvature, and related SVI-JW parameters. It proposes approximating the change in implied volatility with a first-order expansion in those…
The document proposes valuing the principal floor embedded in an inflation-linked bond by treating the consumer price index as an underlying asset and the floor as a put option. When traded inflation floor instruments are unavailable, it suggests estimating…
The document explains why a Black–Scholes cash-or-nothing call can be priced below 50% even when the underlying is above the strike. Its central point is that the model uses a lognormal distribution for the future price, whose positive skew means the…
The document asks whether historical data can estimate American put premiums in the same way that expiry payoffs are used to estimate European put premiums. It proposes replacing the expiry return with the minimum return during the option’s life, then…
The document discusses what can happen to expiring put options when the underlying security remains halted, using RSX options as the motivating case. It summarizes an Options Clearing Corporation policy: when the clearinghouse knows by expiration Monday that…
The note gives an intuition for how the Heston stochastic-volatility parameters correlation and volatility of volatility affect implied-volatility shape. It frames the smile through the risk-neutral distribution: heavier tails raise out-of-the-money option…
The document presents a QuantLib setup for pricing a vanilla European call and obtaining delta, gamma, vega, and theta. The example specifies market inputs, dates, yield and volatility curves, an option payoff and exercise date, then connects them through an…
The document clarifies that volatility is defined relative to a model and, in the Black–Scholes setting, describes the standard deviation of log returns per square root of time. It derives a confidence interval for log returns using normal quantiles, then…
The document considers selling a nearer-dated straddle and buying a later-dated one to gain exposure to volatility over a future period. This is described as an options calendar spread: approximately offsetting deltas can limit immediate directional…
The document asks whether option open interest and trading-volume changes can be incorporated into pricing models or used to forecast asset prices. It connects the question to supply and demand, implied volatility, option Greeks, and trader commitment,…
The document asks how to assess the accuracy of SABR implied volatility surfaces for a chosen equity index and historical period. Its proposed approach is to calibrate SABR, obtain the model’s implied volatilities, and compare them with historical volatility…
The response addresses several interview-style questions about option risk. For a delta-hedged short call, it identifies negative gamma: large moves in either direction are harmful, while smaller moves can help, with volatility changes offering a related way…
The discussion considers why dual range accrual notes may reference a long-minus-short swap-rate spread, such as the 30-year minus 2-year rate, alongside a separate swap rate. It distinguishes risk-neutral pricing probabilities from historical frequencies:…
The document asks how to interpret references to foreign-exchange grid changes in stress testing. It gives an example in which day-to-day stress moves in the U.S. dollar are linked to vanilla EUR/USD options positioning: long strike positions expire while…
The document raises a notation and interpretation question about the market price of risk in the Heston stochastic-volatility model. In the expression discussed, one component depends on the instantaneous variance through its square root, while another…
The document explains why the risk-neutral probability in a binomial option tree can fall outside the zero-to-one range. In the risk-neutral formula, the probability depends on the up and down factors and the risk-free growth over one time step. For it to…
The document discusses why Black-Scholes Greeks remain common in vanilla option risk management despite the availability of stochastic-volatility models. One response favors using hedge sensitivities consistent with the model used to price trades, noting…
The document describes the Breeden-Litzenberger relationship, which obtains a risk-neutral probability density from the second derivative of European call prices with respect to strike, adjusted by the discount factor. Since market prices are available only…
The document distinguishes the probability implied by an option model from uncertainty about whether that model is correct. Under a specified risk-neutral measure and pricing model, an in-the-money probability is a model-implied quantity; gamma does not…
The document introduces speed, the change in gamma as the underlying moves, and color, the change in gamma over time, then asks how traders might capture such higher-order sensitivities. Its answer focuses on gamma scalping: establish a delta-neutral,…