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 addresses how to adjust an implied-volatility surface when its quoted option prices contain small butterfly arbitrage violations. The specific issue is a discrete set of call prices across strikes that fails convexity, which can undermine later…
The document compares non-callable bank certificates of deposit with brokered CDs, focusing on the bank CD holder’s ability to withdraw early at par while paying an early withdrawal penalty. It models that feature as an American-style put embedded in a…
The document poses a fixed-income valuation question about a pay-fixed interest rate swap held for a year. It asks how a positive mark-to-market on the remaining swap, calculated as the difference between the original forward rate and the prevailing…
The document is a brief request for an introductory explanation of the constant elasticity of variance (CEV) model, including its dynamics, strengths and weaknesses, applications to payoff types or hybrid models, and calibration. The response does not…
The document asks how to interpret the Longstaff–Schwartz least-squares Monte Carlo method for pricing American options, especially how its regression target relates to the backward recursion described by Tsitsiklis and Van Roy. The central distinction is…
The document examines how often to rebalance a delta hedge for a European call under Black–Scholes assumptions and geometric Brownian motion. The questioner estimates the local hedging error from the option’s gamma and the squared price move, while…
The document asks how to price an American-style Asian option whose exercise payoff uses the average underlying price over a recent rolling window. It explains why early exercise and path dependence complicate standard approaches: Monte Carlo and tree…
For European call and put options in a model that includes a continuous dividend yield, the zero-dividend case can be obtained by setting the yield parameter to zero. The response also points to a separate list of formulas, though it does not reproduce those…
The document considers how interest rate forwards and swap floating legs change when their fixing dates differ from standard market conventions. It compares FRAs for the same accrual period with fixings at different lags and asks whether separate curves are…
The document explains why a forward-starting swap rate can be approximated from two spot-starting swap rates. In the example, the rate for a swap beginning after three years and lasting two years is estimated from the five-year and three-year spot swap…
The document explores whether option delta should be compared with the option’s purchase price to estimate how a small underlying move affects the position’s return in percentage terms. It contrasts two in-the-money calls on the same hypothetical stock, with…
The document discusses estimating a U.S. corporate bond’s price during London morning hours, when the U.S. bond market is closed. It proposes decomposing the bond into interest-rate and credit components, using the USD swap curve rather than Treasury rates…
The document explains how to establish that a forward measure is a probability measure by weighting the risk-neutral measure with a positive, normalized random variable. It defines the measure of an event as the expectation of its indicator multiplied by the…
The document asks how to evaluate an integral involving a utility function, a cumulative probability, and a decision-weighting function. The response explains that the expression cannot generally be evaluated without explicit definitions of these functions…
The document asks how a forward premium quote for an interest-rate cap relates to the usual spot premium. It describes the distinction as whether the caplet payoff is discounted to its payment date: the spot-premium expression includes a discount factor,…
The document examines why the yield inferred from a Treasury note futures contract can differ from the quoted yield on the on-the-run ten-year Treasury, and asks how futures carry affects DV01 calculations. The response attributes the gap to the difference…
The document asks whether Bermudan swaptions have a put–call parity relationship, how to think about optimal exercise, and whether one side’s decision to exercise determines the other side’s choice. It also considers a callable payer swap with opposing…
The document explains how the at-the-money level for an interest-rate cap or floor is determined and why volatility quotes are often organized around it. The relevant level is the forward swap rate for a swap with the same maturity, schedule, and other terms…
The document explains the drift term used when simulating a stock price under the risk-neutral measure to price a European call by Monte Carlo. The simulated log return has mean (r − σ²/2)T and a random component scaled by volatility and the square root of…
This question asks how to transform implied volatilities indexed by strike and expiry into a surface indexed by delta and expiry. It highlights an apparent ambiguity: two options at the same expiry can appear to have nearly identical deltas while carrying…
This discussion examines a claim that stochastic integrals lack a pathwise meaning, making portfolio gains hard to interpret for a realized asset-price trajectory. The questioner suggests that knowing an integral’s probability distribution might make its…
This short question raises a central issue in option replication: transaction costs make the market incomplete, and asks what Leland’s modified volatility contributes to pricing and hedging. It also asks whether using that adjusted volatility allows an…
The document considers splitting a Monte Carlo pricing workload across threads, running smaller simulations in parallel, and averaging their net present values. The accepted response says this can work, while recommending that threads avoid sharing objects…
A short-rate model specifies stochastic dynamics for the instantaneous interest rate. Zero-coupon bond prices are derived from those dynamics as risk-neutral discounted expectations, and observable bond prices or cash rates provide the market data used to…