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 describes a workflow for pricing interest-rate caps at multiple valuation dates with QuantLib. It builds yield curves from dated market data, interpolates cap volatilities across maturities, then creates Euribor-linked cap instruments and prices…
The document develops a definition of realized gamma from the second-order term in an option’s price change. It defines gamma dollars as one half of spot squared times option gamma, then uses the diffusion component of spot’s change to show that the option’s…
The document answers which exchange rate to enter as the spot parameter when pricing an FX option with the Garman–Kohlhagen model. Its central point is to use the current spot rate; the forward rate for the option’s expiry is already implied by the model’s…
The document explains why applying Itô’s lemma to a function of a diffusion requires a second-order term. For a process with drift and Brownian volatility, a Taylor expansion includes the squared process increment. Ordinary time increments have negligible…
The document questions a claim about compounding a constant overnight rate over a three-month period when calculating a spot swap’s roll-down. The questioner interprets the quoted rate as an annualized overnight rate and compounds it daily, finding that the…
The document explains how to identify the standardized random increment in a risk-neutral trinomial asset model and connect it to a weak convergence argument for Black–Scholes. Taking logarithms of each of the three possible one-step multipliers gives three…
The document describes a discrepancy between a closed-form price for a geometric Asian call and a Monte Carlo estimate. The author uses a formula parameterized by spot, strike, maturity, volatility, interest rate, and a monitoring count, and reports that the…
The document reviews a Monte Carlo implementation for a payoff capped at an upper barrier and floored at a lower barrier at expiry. The accepted answer identifies errors in the simulation: each price update should multiply the current spot by the geometric…
The document explains how a European call behaves in the Black–Scholes setting when volatility is zero. With no dividends, the stock follows a deterministic path growing at the risk-free rate. The call’s payoff is therefore known at expiry; discounting that…
The document explains how to turn a Dupire local volatility model into a European option price. Its example starts with an implied volatility surface, constructs a Black–Scholes–Merton process that uses the surface, and sets up a vanilla call. It then…
The document explains why option pricing can use an equal-probability illustration for upside and downside outcomes even when historical returns are asymmetric. It distinguishes the risk-neutral measure used to price derivatives from historical return…
The document works through the time-zero value of a claim in a one-period, two-state market. A portfolio holding the risky asset and a bond is chosen so that its terminal value matches the claim in both the up and down states. The hedge ratios are obtained…
The document considers how to derive a pricing PDE for a derivative under the Heston–Hull–White model, where the stock, stochastic variance, and short rate are correlated. It identifies a problem with applying the usual discounting transformation directly:…
The document examines how to calculate vega sensitivity under the Basel Fundamental Review of the Trading Book standardized approach. The question contrasts multiplying Black–Scholes vega by implied volatility expressed as a decimal with an example using a…
The document discusses two interest-rate products that pay based on absolute changes in future rate volatility. One references successive six-month LIBOR changes; the other references changes in a long-dated forward-start swap rate and includes capital…
The document poses a static arbitrage problem using a contract that pays a negative logarithm of the terminal underlying price, a forward contract, and a discount bond. Given prices for the three traded assets, it infers the underlying’s spot value from the…
The document asks why Laguerre polynomials are used as regression basis functions in Longstaff–Schwartz Monte Carlo pricing of American options. It cites discussion of multicollinearity among basis functions and a separate numerical comparison that found…
The document asks how to implement Rebonato’s approximation for swaption volatility in C++. The formula combines swap weights, forward rates, correlations, and the integrated products of forward-rate volatilities. With piecewise-constant volatilities, each…
The document clarifies the maturity value of a money market holding that is worth K multiplied by a discount factor at time t. Because the amount is invested in an account earning the risk-free rate, its value grows from time t to T by the corresponding…
Antithetic sampling pairs each simulated random draw with a complementary draw, such as transforming a uniform probability by taking its complement. For normally distributed inputs, this produces paired values with equal and opposite standardized shocks.…
A defaultable bond’s market price reflects interest rates, the probability of default, and the value expected after default, represented by recovery or loss given default. The relative influence of these factors changes with credit quality: interest rates…
The document outlines a framework for measuring corporate bond credit risk through CDS spreads. It describes deriving default and survival probabilities from CDS quotes, then pricing bond cash flows with risk-free discounting and a recovery component. Since…
The discussion asks whether a binary option always has a Black–Scholes implied volatility and presents several competing answers. A binary call price can rise and then fall as volatility increases, so an observed price may correspond to two volatility…
The document asks whether swap rates with different fixed-leg payment frequencies should be adjusted before bootstrapping zero curves intended for comparison. It contrasts annual fixed payments for euro swaps with semiannual fixed payments for US dollar…