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 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 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 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 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…
The document asks whether binary options can produce a position that doubles on success and halves on failure when the event is close to equally likely. Its algebra shows that the desired payoffs imply a particular option quantity and purchase price, but…
The document addresses how to revalue an options portfolio in a Monte Carlo VaR simulation when the underlying is simulated with a historical stochastic-volatility model such as GARCH. Its central distinction is that historical volatility of the underlying…
The document answers how to select the at-the-money strike when calibrating the volatility level in a shifted SABR model. The shift is added to both the forward and strike in the model’s implied-volatility calculation. Consequently, an option that is at the…
The document considers a borrower’s option to choose between a fixed-rate loan, a floating-rate loan, or cancellation after a decision window. It frames the choices as embedded options with value linked to the borrower’s credit spread, interest rates, and…
The document presents a question about implementing the pathwise derivative method for estimating a call option’s delta under a geometric Brownian motion model. The proposed simulation code evolves prices through multiple time steps and then sums…
The document considers a simplified model for valuing inflation options embedded in inflation-indexed contracts with guarantees. The author already has a stochastic nominal interest-rate model, G2++, and wants inflation scenarios linked to it. One proposed…
This discussion examines why longer-dated options can cost more even when implied volatility appears to fall with maturity. It cautions that implied volatility term structures vary: they may rise, fall, or fluctuate, including at the money. In the…
The document compares a one-touch option, which pays when the underlying crosses a threshold at any time through maturity, with a binary option that pays when the underlying is above the threshold at maturity. It reports that the one-touch price is…
The document considers why a riskless portfolio formed from an option and a hedge in the underlying must earn the risk-free rate in a binomial pricing model. The answer frames the argument as a contradiction: assume an arbitrage exists, then show that…
The document distinguishes calculating implied volatility from choosing coordinates for interpolation and display. To calculate implied volatility from market prices, supply the actual spot, strike, maturity, rates, and dividend yield required by the pricing…
The document addresses whether the vanilla option portfolio used to replicate a variance swap still applies when the underlying pays dividends and the risk-free rate is nonzero. Its answer says the replication formula remains valid, provided the forward…
The document explains why a long position in a standard European vanilla option generally has positive vega, even when the option is already in the money. Vega measures how an option’s value responds to a change in volatility. The key idea is that a vanilla…
The document addresses a common gap in the delta-hedging derivation of the Black–Scholes PDE: specifying a stock holding does not by itself explain how the portfolio remains self-financing as that holding changes. A trading strategy is described through its…
The document explains how the Black formula for a European option on a futures price relates to Black–Scholes pricing. Under risk-neutral pricing, the futures price is modeled as a lognormal process, and the option value is the discounted expected payoff at…
The document derives an equivalent martingale measure for a Bachelier stock-price model with constant drift and volatility, assuming a zero interest rate. Under the original measure, the stock follows an arithmetic Brownian motion. To make the discounted…