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
This question describes a Monte Carlo implementation of the Libor Market Model (LMM) for simulating forward rates before a swaption’s exercise date. The model uses an initial forward curve, a correlation matrix, and time-dependent volatilities, with…
The document proposes a staged way to learn Monte Carlo methods, while emphasizing that the right material depends on the problem. It starts with simple simulations such as dice, coin tosses, estimating areas, and pricing a vanilla option. It recommends…
The document concerns Monte Carlo valuation of a barrier option when the underlying follows a jump-diffusion process. The question reports a simulated value that differs from the cited paper and jump probabilities that sometimes fall outside the valid…
The document diagnoses a QuantLib error raised while building a Black variance surface from option implied volatilities. The reported validation requires expiry dates to be unique and arranged in chronological order. In the supplied schedule, one-year expiry…
For standard European calls and puts, the document explains why a higher ask price usually implies a higher ask implied volatility than bid implied volatility. The key link is that, holding other inputs constant, these option prices increase as volatility…
The document asks whether a derivative can have a payoff that is quadratic in the underlying asset’s price, including a version floored at zero. The responses explain that a bespoke payoff could be requested from a bank, while emphasizing that the buyer…
The document asks whether European call prices at a single maturity uniquely determine a time-independent local-volatility function, given that Dupire’s formula ordinarily uses a surface across maturities. One answer cites a result establishing a unique…
The document distinguishes the risk-reversal trading strategy from the market convention used to quote a risk reversal on a volatility surface. A risk reversal combines a call and a put, often selected at specified delta points, while the quotation…
The document explains why the stock price and the value of interest-bearing cash satisfy the Black–Scholes pricing PDE. The stock itself is a traded asset whose value is the underlying price, while a bank balance grows deterministically at the risk-free…
The document compares the spot sensitivities of American and European calls when the stock pays a single dividend before expiry and interest rates are zero. It represents the American call as the expected value of the better choice at the dividend date:…
The contract pays the positive part of the difference between the stock price at an earlier date and its price at maturity. At the earlier date, the strike is known, so the claim becomes an ordinary European put with a strike equal to that observed stock…
A binary option pays a fixed amount when the underlying finishes on one side of its strike, so its value is tied to the risk-neutral probability of that event, discounted for interest rates. Under a lognormal Black–Scholes model, increasing volatility can…
The response distinguishes historical par spreads from modern standard CDS market quoting. Par spreads describe the spread associated with a contract that has no upfront fee, as used before the 2009 CDS contract changes. Current trading generally uses a…
The document addresses a kink that can appear when combining call and put implied volatilities to build a fixed-tenor smile from American SPY options. The response recommends deriving one forward price for the option maturity from dividends and the market…
An interest rate swap’s current value can be calculated from the yield curve, without specifying a stochastic model for future rate movements. That valuation answers what the swap is worth now under the curve and arbitrage-free pricing conventions; it does…
A replicating portfolio matches an option’s payoff only under idealized assumptions, including continuous trading, no transaction costs, unlimited divisibility, and known constant volatility. Actual markets violate these conditions, so an option combined…
Whether an option has a closed-form price depends on both its payoff and the assumed dynamics of the underlying asset. Some European vanilla options have tractable formulas under certain models, while other combinations of payoff and dynamics do not. The…
The document shows how a payer swaption can be expressed as an option on a coupon bond. It starts from a fixed-for-floating swap with reset and payment dates, writes its value as the difference between a floating leg and a fixed leg, and uses the forward…
The document explains how to hedge the foreign exchange component of P&L from American or global depositary receipts. An ADR position reflects both the local-currency value of its underlying equity and exchange-rate movements. A portfolio can aggregate its…
The document addresses a common sign confusion in put-call parity: when constructing a synthetic forward by buying a call and selling a put at the same strike, the put’s premium is not itself negative. Option premiums are positive prices by definition;…
The document clarifies the probability terms in the Heston call pricing formula. It decomposes the call payoff into two expectations, then uses a change of numéraire to express the price through probabilities under the risk neutral measure and a stock…
The document considers the issuer’s exposures on an autocallable note linked to the FTSE 100. The note has annual autocall observations, a coupon that accumulates until autocall, a maturity date, and a downside knock-in barrier observed at maturity. The…
This question describes fitting a probability distribution for an asset’s terminal price to discrete option quotes. It proposes using a distribution inferred from market implied volatilities as a prior, then minimizing relative entropy from that prior…
The exchange presents a regression-based way to estimate how implied volatility may change when the underlying spot price moves. It points to a minimum-variance delta relationship in which the expected implied volatility change depends on the proportional…