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.
10,263 documents
The document asks how to calibrate a SABR volatility surface for S&P 500 index calls when the beta parameter is fixed in advance. The choice is between fitting alpha, rho, and nu separately for each expiration or fitting one parameter set across the full…
The response gives practical guidance for building an implied volatility curve when calls and puts with the same delta show different volatility estimates. It recommends averaging call and put implied volatilities for at-the-money options, while using…
The discussion compares a bridge-based design from a derivatives-pricing C++ book with a simpler polymorphic class hierarchy managed through smart pointers. The bridge wraps an implementation object, delegates calculations to it, and handles its lifetime.…
The document presents stochastic-calculus exercises involving a Hull–White short-rate process, a default-free zero-coupon bond, and a dollar–yen exchange rate. One task asks for the dynamics of a Japanese investor’s bond value after converting it into yen,…
The document shows how to model a private equity clawback when the value relevant to limited partners consists of a risky net asset value component and a fixed amount of past distributions. It represents the net asset value as a geometric Brownian motion and…
The document explains how no-arbitrage reasoning bounds the price and strike sensitivity of a vertical call spread. For strikes K1 < K2, the spread formed by buying the lower-strike call and selling the higher-strike call has a payoff between zero and K2 −…
The document raises questions about local volatility models used for equity derivatives. It asks why forward smiles under local volatility are said to become flatter and higher, whether the model’s calibration to an initial volatility surface makes its…
The discussion derives the stochastic differential of the exponential density used in a Girsanov change of measure and explains its connection to the stochastic exponential of a continuous local martingale. The key correction is that replacing the stochastic…
The document derives the self-financing portfolio interpretation of a vanilla call when the stock is used as numeraire. Starting from a martingale representation for the call price divided by the stock, it applies Itô's formula to relate changes in the…
The document explains an adapted stochastic process in financial mathematics through the information represented by a filtration. At each time, the process value must be measurable with respect to the sigma algebra available at that time. Intuitively, this…
The document asks which market instruments can help construct the short end of the SOFR curve, given the questioner’s impression that swaps are unavailable below a one-year maturity. The response points to trading in one-month and three-month SOFR futures.…
The document raises a question about simulating future interest-rate forward curves under a T-forward measure. It contrasts centering a simulated rate at its expectation under the measure associated with time t with using the forward rate observed at the…
The document considers buying a call and selling a higher-strike call below the spread’s theoretical value, then delta-hedging through expiry. One response says that under Black–Scholes dynamics, with the hedge using the true volatility, the initial pricing…
The document poses a derivatives-pricing question: how to value a maturity payoff equal to the inverse of a non-dividend-paying stock price assumed to follow geometric Brownian motion. The proposed approach starts with the stock’s risk-neutral dynamics,…
The note addresses an apparent funding gap when rebalancing a short call hedge as time passes and the underlying price stays unchanged. Its answer uses the Black–Scholes pricing equation with zero interest and dividends, where theta offsets the gamma…
This note explains why self-financing is a basic condition for admissible hedging and arbitrage strategies. A portfolio is self-financing when purchases of new holdings are funded by selling existing holdings, rather than by injecting or withdrawing outside…
The note derives two CAPM asset-pricing forms: discounting an expected payoff by a risk-adjusted required return, and discounting a risk-adjusted expected payoff at the risk-free rate. It starts with the CAPM expected-return equation and relates an asset’s…
The document asks how VIX futures can keep trading when a circuit breaker halts SPX options and prevents the VIX index from being calculated, especially if the halt overlaps the March contract’s valuation date. It raises the possibility of estimating…
The document frames a modeling question about replacing deterministic correlations with stochastic correlation matrices in a multi-factor fixed-income model such as a LIBOR market model. It argues that fixed correlation may be adequate for short-maturity…
The document explains why a floating swap leg does not always become independent of day-count conventions, even when the accrual fraction appears to cancel between the coupon amount and the forward rate. That cancellation requires the day-count fraction used…
The document describes an attempt to price a euro zero-coupon inflation swap in QuantLib and reconcile the result with Bloomberg. The author reports that prices are close when the swap dates fall on whole-year anniversaries of the valuation date, while…
The document asks whether variance swaps on interest-rate swap rates are actively traded and liquid, comparing them with the more familiar equity variance swap market. The response offers a brief market-liquidity observation rather than a pricing method or…
The document collects book recommendations for an algorithmic trading programmer who wants to connect basic options theory with the language and practice of volatility trading. Recommendations include introductory treatments that emphasize intuitive option…
The document explains why vanilla calls and puts can show the same asymmetric volga profile, with larger values for in-the-money calls and out-of-the-money puts. It uses the Black–Scholes expression for volga, which combines vega with a term based on d1 and…