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 considers pricing a European option when the underlying asset’s daily return is constrained to a fixed interval. It proposes replacing the usual return density with a two-sided truncated normal risk-neutral density, then valuing the option by…
The document contrasts rational exercise models with behavioral approaches for embedded options, such as mortgage refinancing rights and callable corporate debt. Borrowers and issuers may exercise based on private circumstances, including personal finances…
This question asks how SABR is used in practical option workflows. It contrasts fitting or interpolating a volatility surface with SABR to obtain Black implied volatilities, then managing positions with Black Greeks, against measuring and managing risk…
The document explains how to express a Bachelier caplet as the difference between an asset-or-nothing payoff and a cash-or-nothing payoff. Under the stated forward-measure setup, the cash digital component is proportional to the strike times the probability…
The document asks for a more accessible derivation of the semi-closed-form price of a European call under the Heston stochastic-volatility model. It does not derive the pricing formula itself; instead, the replies point readers toward a paper with a…
The document raises a question about P&L attribution for a single stock option. It defines daily P&L as the change between desk market values and proposes explaining that change through underlying-price delta and gamma effects, implied-volatility vega, and…
The document asks how to close an in-the-money American put in a limited-margin IRA when the option has poor liquidity, uncovered options and short stock positions are prohibited, and exercising would forfeit remaining time value. It considers buying a…
The response explains why a volatility surface matters when pricing a Bermudan swaption, an option exercisable on specified dates. It first clarifies that a Bermudan contract need not be exercisable from the beginning of its life, then outlines a model-based…
This note shows how to price a path-dependent lookback call in a two-period binomial model. A European payoff depends only on the terminal asset price, so the two paths that reach the same middle terminal node can be combined and their probabilities added. A…
This note explains how to connect a Black–Scholes call’s volatility sensitivity to the strike derivative used to price a cash-or-nothing digital option. It starts from the call price and its vega, then shows that the apparent mismatch between a term…
The exchange addresses how to obtain the underlying input needed to analyze an options dataset when spot prices are unavailable. It suggests estimating a forward price from put and call quotes at a common maturity: identify the strike where their prices are…
A special cash dividend or another corporate action can change an option contract’s deliverable. As a result, an adjusted, nonstandard contract may appear beside a newly issued standard contract with the same underlying, strike, expiration, and call or put…
The document discusses how to hedge a caplet dynamically in a theoretical framework, comparing it with delta hedging an equity call. One suggested approach is to use a forward rate agreement with the relevant expiry, such as an at-the-money FRA, and adjust…
The discussion examines why the variance sensitivity of a variance swap may seem inconsistent with the sensitivities of the options used to replicate it. Under assumptions of continuous paths and a continuum of strikes, the question treats the option…
The discussion asks whether Bitcoin has a quantifiable fair value and how mispricing might be recognized. The answers describe its traded price as an outcome of supply and demand once the market is sufficiently liquid, while emphasizing that speculation is…
The document raises a practical calibration problem: fitting an SVI or SABR volatility surface to mid implied volatility produced a satisfactory fit, while separate fits to bid or ask implied volatility performed poorly. It asks how to fit surfaces to…
The document asks how to value a cancelable swap whose termination payment is linked to an index, then isolates the question of choosing when to pay an index-based amount. The provided answers treat the simplified payment as a scaled forward-like payoff and…
The document considers how to describe option risk across an implied volatility surface. Standard Black–Scholes Greeks measure sensitivity to model inputs, but Vega is difficult to aggregate across options because an implied volatility move need not be…
The document explains why a smile that bends down or up around the forward does not, by itself, establish whether option prices admit arbitrage. Smile curvature is related to the shape of the implied risk-neutral distribution: a concave smile can accompany a…
The document addresses whether Black-Scholes time to expiration should be measured in trading days or calendar days when volatility is estimated using trading-day data, and asks how the risk-free rate should be treated. One response advises keeping the time…
The document asks how market makers choose bid-ask spreads for options quoted in implied volatility terms. It gives an example of a quote with a one-point gap between bid and ask volatility, and suggests that market volatility and the need to hedge inventory…
The document asks how to price a European option on an amortizing interest-rate swap when market volatility quotes are available only for standard, non-amortizing swaptions. It outlines the usual Black-style swaption valuation using an annuity, forward swap…
The document addresses how to assess an exotic option pricing model when direct market prices are scarce. It proposes first checking whether the contract can be reduced to a simpler exotic structure that has observable quotes; if so, the model should…
The document explains how to derive the Black–Scholes pricing equation from a risk-neutral valuation formula. It assumes the underlying follows a geometric Brownian motion under the risk-neutral measure, with deterministic interest rates and constant…