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 explains why an implicit finite-difference solution to the Black–Scholes partial differential equation can still produce large pricing errors when the log-price grid is too narrow. The equation is defined over an unbounded domain, while a…
The document asks how to represent a portfolio’s vega when its original volatility surface has many strike pillars but the target surface retains only three. Vega is described as distributed across the original grid of maturities and strikes, leaving the…
The document asks how to calculate the probability that a discrete-time lookback put finishes in the money in a Cox–Ross–Rubinstein binomial model. Its payoff depends on the minimum underlying price observed along the path, rather than only the terminal…
The document explains how to specify a three-branch asset-price tree when a single-period move can be up, middle, or down. The three branch probabilities and three move sizes initially leave six parameters. Probability normalization and matching the expected…
The document asks which parametric forms are commonly used to fit implied volatility smiles in VIX markets. It situates the question against SPX options, where the author says stochastic volatility-inspired and surface stochastic volatility-inspired forms…
The document explains how cash-settled options can create payment obligations and distinguishes collateral movements from final settlement. In bilateral or centrally cleared derivatives, counterparties may post margin as valuations change; eligible…
The document clarifies why option volatility models may express moneyness using the underlying’s forward price or spot price. It distinguishes this choice from forward volatility, which means volatility over a future time interval. Forward based moneyness…
The document asks how to state the Black–Scholes free-boundary problem for an American put. It contrasts two proposed condition sets involving the exercise region, continuation region, terminal payoff, behavior at large stock prices, and value and delta…
The document examines a claim that at-the-money-forward implied volatility in the Heston model is below the square root of expected variance. The response connects variance swap volatility to an expectation over squared values of a transformed, or modified,…
The document addresses finite difference pricing when an exotic option has a discontinuous payoff, such as a binary or barrier, and nearby vanilla strikes are used for hedging. A coarse asset-price grid may fail to represent the payoff boundary accurately…
The document surveys modeling concerns when interest rates can fall below zero, focusing on products whose pricing frameworks assume lognormal rates. Black-style option formulas and some volatility conventions become unsuitable when rates may be negative.…
The document describes a question about Levy's moment-matching approximation for Asian options under geometric Brownian motion. When some monitoring points have already been observed, the method adjusts the strike using the observed average and the share of…
The discussion estimates the one-day profit and loss of a short call when the underlying moves sharply. The answer first assumes the position is delta hedged, so the starting portfolio has no first-order exposure to the spot move. It then treats the stated…
The document explores delta and vega hedging, exotic-product risk, and pricing when a derivative references an investment fund. The question highlights practical constraints: fund shares may be difficult or impossible to short, listed options may be…
The document asks which securities offer options expirations more often than monthly, motivated by a strategy of buying near-the-money calls when little time value remains close to expiration. It notes that many U.S. stock options expire on the third Friday…
The example shows how an incomplete one-period trinomial market can produce multiple risk-neutral probability distributions and a range of prices for a European call. With three possible stock outcomes but only the probability-sum and discounted…
The discussion clarifies which expiry to use when applying a Black-style model to an option on a VIX future. It says to use the option’s exchange-published expiration date, measured from the valuation date, rather than the maturity of the underlying futures…
The document asks how to identify, from a stock universe, the three names likely to produce the highest premium for a worst-of put. Its payoff depends on the weakest normalized asset outcome at maturity, so the question concerns both individual price…
The document considers whether shorting an out-of-the-money option and hedging only when the underlying reaches its strike can reproduce the option payoff or cap losses at the premium received. It describes a stop-loss/start-gain approach: the hedge is…
The exercise asks whether the reciprocal of an asset price can itself be the arbitrage-free price of a traded derivative, and how to value a claim paying the reciprocal at maturity. Its attempted valuation uses risk-neutral discounted expectation under…
The document describes a one-expiry SPX implied-volatility calibration using the SSVI parameterization. The initial implementation produced implausible estimates when fitting market option prices, and the author also found that the fitting objective had…
The document explains how to simplify a maximum-and-minimum expression involving two ordered strikes and a terminal asset price. One proof divides the possible price outcomes into three regions: below the lower strike, between the strikes, and above the…
The document asks why a single-look CMS cap and a CMS floor with the same expiry and at-the-money strike can show different vega exposures. The observation comes from pricing a ten-year-expiry CMS30 cap and comparing it with the corresponding floor. The…
The document explains a first-pass way to approximate a payer swaption’s profit and loss for a move in the underlying swap rate: use a Taylor expansion. Delta represents sensitivity to a parallel shift in the swap curve, while gamma captures convexity. This…