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 presents an options-arbitrage exercise involving European calls and puts with the same strike and expiration. Given a stock price, interest rate, and equal quoted option prices, the question is how to identify a risk-free trade using put-call…
The document raises questions about how option delta and dual delta compare across strike prices, and whether either can represent the probability that a call expires in the money. It also asks whether gamma and dual gamma show a consistent relative pattern…
The document discusses simulating a stock price under Merton’s jump-diffusion model for pricing Asian and digital options. Its setup combines a Brownian diffusion with jumps whose count follows a Poisson process and whose log jump sizes are normally…
The discussion considers why quantitative finance may appear to use less advanced mathematics than physics. It argues that mathematical sophistication alone does not drive useful research: a strong idea can make major contributions with relatively accessible…
The document explains what happens to a bull put spread when the position size increases. The example sells a higher-strike put and buys a lower-strike put, with stated premiums for both options. Increasing both legs from one contract to ten leaves the…
The document explains that an empirical volatility surface is built from market prices of vanilla options. Those prices can be expressed as Black–Scholes implied volatilities across strikes and expirations, producing a surface observed at the time of…
The document discusses selecting option implied volatilities and strikes as inputs or starting values for calibrating the Heston stochastic volatility model. It raises whether a one-year implied volatility is appropriate for the model's long-run variance…
The discussion presents a method for pricing a maturity-only payoff defined as the minimum of two linear functions of the terminal stock price. It advises plotting the payoff against the terminal price, identifying where its slope changes, and using those…
The document considers implied volatility for an American-style option on a short-term interest-rate future. It starts with a Bachelier normal model as a European-option approximation, then asks how to adapt a binomial tree for early exercise. The discussion…
The note clarifies that the symbol S in the discussed Black–Scholes derivation refers to the current spot price, written as S at time t. It connects that interpretation to geometric Brownian motion, where the asset price changes through a drift component and…
The document describes how to value a European bear put spread, including one embedded in a contingent value right. The position consists of a long put at the higher strike and a short put at the lower strike. Under the Black–Scholes framework, price each…
The document gives the Garman–Klass estimator for historical volatility using daily open, high, low, and close prices. For each observation, it combines the squared logarithm of the high-to-low ratio with a weighted squared logarithm of the close-to-open…
The document challenges the claim that a large amount of in-the-money call open interest creates a large supply of shares at expiration and therefore predicts a sharp decline. It explains that each open option contract has both a long and a short side.…
The document considers extending a constant-volatility trinomial stock option model to use a deterministic, time-varying interest rate curve. The suggested approach is to set the rate for each time step so that its discount factor matches the curve over that…
The document explains why the Black–Scholes–Merton model implies log-normally distributed asset prices at maturity and normally distributed log returns. It traces this result to the model’s assumption that price changes follow a generalized Wiener process…
The document describes an Interactive Brokers API issue in which reported call option bids, asks, and deltas appeared inconsistent with the quoted price of an S&P futures contract. The initial request used a regular equity index option contract, even though…
The document explains why an option on a spread of two futures cannot generally be replicated statically using options on the individual futures. It uses a gasoline crack spread option as an example of this contract type. The proposed approach is to price…
The document considers valuing a written put whose exercise price depends on the company’s EBITDA, net debt, and minority shareholders’ ownership percentage at exercise. Because the strike depends on future company information, it is not a fixed-input…
The document explains why option prices can be used to infer a risk-neutral probability distribution, but do not directly reveal real-world probabilities. The risk-neutral measure combines physical probabilities with the stochastic discount factor, which…
The document discusses how to select an implied volatility for a fixed-strike Asian put with discrete averaging in a Black–Scholes setting. A simple practical choice is the volatility at the option’s expiry from the vanilla volatility surface; this can…
The document investigates why QuantLib’s daily valuations of a short-dated FX option diverge from Bloomberg on some dates, despite matching on several others. The accepted answer identifies differing date conventions: Bloomberg distinguishes the pricing…
The document compares the price of a European call written on a one-dollar cash account when the discount factor is stochastic with the price under a deterministic discount factor having the same expectation. It expresses the random-rate call payoff using…
The document considers whether a European put’s no-arbitrage price bounds imply that its value must fall toward zero as time to maturity becomes very large. The stated lower bound is the discounted strike minus the spot price, while the upper bound is the…
The document explains a risk in interpolating implied volatility linearly across option expiries. The key no-arbitrage condition is that total implied variance, defined as maturity times implied volatility squared at a given strike, should not decrease with…