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 explains why changing short-rate volatility can affect an interest rate swap’s value in the Ho–Lee model, despite the intuition that swap pricing depends on current zero-coupon bond prices. It presents the short rate as a drift term plus a…
The document explains that Black-Scholes-Merton remains common in practice for European options, including settings where markets quote volatility and the model converts that volatility into prices. It also notes that exchanges may use Black-Scholes variants…
The document presents a question about recovering call prices from observed SPX put prices using put-call parity, with zero interest rates assumed. It supplies mixed call and put quotes, option types, and increasing strike values, then points to cases where…
The document describes two ways to explain daily profit and loss by fully repricing a portfolio as market inputs move from prior-day to current-day values. In the cumulative, or waterfall, method, inputs are changed sequentially and each price change is…
The document explains how the ISDA CDS calculator handles a contract that was originally traded in the past but is now being valued with less time to maturity. The calculator is a pricing model, not a historical or current spread database, so the user must…
The document explains how option writers may manage exposure before expiration through delta hedging. In the simplified account, they hold a changing mix of the underlying stock and financing assets, adjusting that mix as the option’s sensitivity changes.…
The document explains how an empirically calibrated SVI volatility surface can support option pricing and Greek estimates. SVI maps maturity and strike to an implied volatility; that volatility can then be supplied to a Black–Scholes routine to obtain a…
The document asks whether interest rates in binomial and continuous-time pricing models can be stochastic while still allowing a change to a risk-neutral measure. Its two-period example treats the rate as an additional random outcome that is not determined…
The document asks how to expand a financial stochastic differential equation when the diffusion coefficient depends on both the underlying price and a stochastic volatility factor, as in a SABR-style model. It contrasts this setup with simpler stochastic…
The document explains why implied volatility often rises away from the at-the-money strike, drawing on three complementary interpretations. One links smile curvature to higher moments of the return distribution: convexity can reflect positive excess…
This QuantLib discussion investigates why a newly constructed Treasury bond does not return exactly par when priced at a coupon date using a flat yield. The example is a long-dated, semiannual fixed-rate bond with a 2% coupon and a 1% annual yield. The…
The document derives an expectation involving the terminal stock price multiplied by an indicator that the stock finishes above a strike. It shows how to evaluate the risk-neutral expectation directly by integrating the lognormal stock distribution, without…
The document explains the interest rate convention used in an implied volatility approximation and how to estimate an asset’s forward price. It treats the constant interest rate as the annualized risk-free rate, assuming the rate used in the approximation…
The document asks why a foreign-currency forward can be treated as a linear instrument for value-at-risk analysis. The quoted textbook framing represents a forward to buy foreign currency as a long position in a foreign bond and a short position in a…
The document derives a closed-form price for a European currency call when domestic and foreign interest rates follow Hull–White dynamics and spot FX has constant volatility. It changes from the domestic risk-neutral measure to the domestic maturity-forward…
The document shows how to establish a product identity for stochastic exponentials of continuous semimartingales. It starts with processes whose stochastic exponentials solve differential equations of the form dZ = Z dX. Applying the semimartingale product…
The note explains how the transition from LIBOR to SOFR affects the optionlets included in a standard one-year USD interest-rate cap. In the LIBOR convention described, the first rate fixing is already known at the start date, so the cap begins with the…
The document describes why valuation of the foreign leg of a mark-to-market cross-currency swap can require a convexity adjustment. It writes the foreign-leg cash flows and explains that the relevant expectation is taken under the domestic measure, while the…
The document asks how a stochastic exponential in a Girsanov theorem example reduces to a formula involving time, a constant market-price-of-risk term, and Brownian motion. The general expression contains integrals of a process θ over time and against…
The document asks how to break an option position’s Vega P&L into contributions from at-the-money volatility, skew, curvature, and related SVI-JW parameters. It proposes approximating the change in implied volatility with a first-order expansion in those…
The document explains how to calculate periodic cash flows and present values for a USD cross-currency basis swap involving three-month and twelve-month LIBOR legs. For each period, it multiplies notional by the accrual fraction and the applicable LIBOR…
The document proposes valuing the principal floor embedded in an inflation-linked bond by treating the consumer price index as an underlying asset and the floor as a put option. When traded inflation floor instruments are unavailable, it suggests estimating…
The document explains why a Black–Scholes cash-or-nothing call can be priced below 50% even when the underlying is above the strike. Its central point is that the model uses a lognormal distribution for the future price, whose positive skew means the…
The document distinguishes geometric Brownian motion from the broader class of semimartingale processes. It explains a semimartingale through a decomposition into a local martingale component and a process of locally bounded variation. In the GBM example,…