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 response addresses early exercise of American calls and puts on a stock that pays a continuous dividend yield. It presents an early exercise premium decomposition: each American option’s value is expressed as its European value plus terms involving…
The document compares quick yield-to-maturity estimates with cash-flow discounting across the zero-coupon curve when pricing corporate bonds. For a bond with large interim coupons or amortizations, a single maturity-based risk-free rate can misrepresent the…
The discussion examines an apparent case in which a numerically calculated American call is slightly cheaper than an analytically priced European call under matching inputs. The accepted response attributes the discrepancy to comparing different numerical…
The document derives the pricing equation for a zero-coupon bond when the short rate follows a Vasicek-style jump diffusion. The rate combines mean reversion, square-root diffusion volatility, and independent Poisson jumps with exponentially distributed…
The document explains how to view a fixed-rate bond that the issuer may redeem on specified dates as a bond plus an issuer-held Bermudan call feature. Unlike a holder-exercised option, the issuer’s exercise decision works against the bondholder, so the…
A credit index can be compared with a portfolio of single-name credit default swaps that references the same constituents on matching terms. If the index and the component portfolio diverge sufficiently in value, the difference, called skew here, may create…
Short-term interest rate futures imply an average reference rate over each contract period. To estimate the rate expected after a central bank meeting, carry the known pre-meeting rate across the days before the meeting, then solve a day-weighted average…
The document explains how to create a zero yield curve in QuantLib-Python when zero rates are already available, rather than first bootstrapping them from market quotes and rate helpers. The accepted answer describes supplying maturity dates, corresponding…
The document distinguishes two connected ideas in no-arbitrage option pricing. Risk-neutral valuation expresses a derivative’s price as the discounted expectation of its payoff under risk-neutral probabilities, linking a payoff to a price. A replicating…
The document clarifies that a partial differential equation’s linearity depends on how it involves the unknown function and its derivatives, not simply on whether volatility is constant. In the heat-equation form presented, the unknown and its time and…
The document investigates why a QuantLib bootstrap for Singapore’s SORA overnight curve matches quoted rates at short maturities but diverges from the input quotes at longer maturities. The proposed diagnosis is a mismatch in floating payment frequency: the…
The document solves a stochastic differential equation in which the level of a process is multiplied by a constant coefficient and a Brownian increment. It identifies the equation as a geometric Brownian motion with zero drift and a negative diffusion…
The question outlines a Monte Carlo approach to option-adjusted spread (OAS) for a mortgage-backed security: simulate interest rates, derive mortgage rates along each path, project cash flows, discount them, average the resulting values, and find the spread…
The discussion asks how to build a static hedge for an up-and-out call on the S&P 500. Its central point is that European options alone generally cannot provide an exact static hedge for a barrier option. A barrier’s payoff depends on whether and when the…
The document explores extending the Heston stochastic volatility model to represent mean reversion in the asset price or returns as well as in variance. The answer proposes a price-level adjustment in which the drift of log price pulls it toward a long-run…
The document examines how volatility affects the risk-neutral probability that an option finishes in the money under Black-Scholes. For a call, that probability is represented by the cumulative normal value at d2, so its response to volatility depends on…
The document explains why a curve is not defined by the fixed or floating legs of a swap. A curve instead supplies discount factors or forecast rates, and those functions must be distinguished when valuing a cross-currency swap. For a fixed-fixed USD-INR…
The document explains risk-neutral pricing through a one-period binomial model with a stock and a risk-free account. When the risk-free growth factor lies between the stock's down and up factors, the model rules out simple arbitrage and defines risk-neutral…
The document raises a question about how to express an FX option’s delta when the trading book uses an accounting currency different from either currency in the option. Its example is a one-year at-the-money EUR call and USD put, with option and rate inputs…
The document outlines a factor-based approach to estimating one-day value at risk for a currency portfolio containing forwards. A forward’s value is affected by its exchange rate and the interest rates of both currencies. For a USD/JPY forward, for example,…
This note explains why a Bloomberg VCUB option matrix may show different values for strike and straddle views. The distinction is the displayed measure: the strike view presents volatility, while the straddle view presents a premium. A premium-based straddle…
The note shows how to use the Gaussian shift theorem to evaluate an expectation involving two correlated standard normal variables. It first states the theorem: an exponential tilt inside an expectation can be converted into a shifted argument of the…
The note explains why a discount rate in discounted cash flow analysis can be viewed as a minimum acceptable return. It frames the rate as a risk-free benchmark: an investor can generally earn that return without taking risk, so a cash flow discounted at a…
The document explains that implied volatility is the Black–Scholes volatility that matches an observed option price; it is a way to express market prices through that model, not proof of a uniquely correct price. It also cautions that the strike pattern…