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 post considers how to decide whether an implied volatility smile has unusually large skew. It defines local skew as the slope of implied volatility against log moneyness, while noting that the raw slope depends on the volatility level and may need…
The post asks for readable resources that build intuition for the Black–Scholes Greeks, especially through visualizations of how measures such as delta and vega change with time and moneyness. It also seeks guidance on using Greeks to structure options…
The question considers insuring a portfolio of large- and small-cap US equity ETFs against a loss beyond a portfolio-wide threshold. It contrasts a single payoff based on the combined basket with separate options on each holding, which could pay when one…
The document explains how put–call parity and strike-spread bounds can determine whether a one-year put with a strike of 100 is mispriced, given a call with a strike of 90, the stock price, and the risk-free rate. It derives the value of the 90-strike put…
The document explains why using the same numerical volatility input in the Bachelier and Black–Scholes models can produce very different call prices. Although both models describe uncertainty in an underlying price, their volatility parameters use different…
The document answers a request for mathematically rigorous foreign-exchange modeling references that also reflect a practitioner quant perspective. Its recommendations focus on books about pricing FX options, modeling smile risk, and valuing structured…
The document considers how to calculate returns for a portfolio combining equities and credit, using an equity index and an investment-grade credit index as examples. It cautions that a credit default swap position does not have a meaningful return from…
The document explains how to extend the familiar Heston characteristic function for log price to the joint distribution of log price and variance at a future time. It first writes the model as a two-dimensional diffusion, using independent Brownian motions…
The document examines the claim that an option’s delta approximates its probability of expiring in the money. In the Black–Scholes framework, the answer connects delta to the risk-neutral probability of an in-the-money expiry, with an adjustment related to…
The document explains how open interest relates to long and short positions in options and other derivatives. Because each contract has both a long side and a short side, open interest can be counted from either side: the number of open longs equals the…
The document explains that a ratio of the swap bid–ask spread to the bond bid–ask spread is not a standard bond-versus-swap spread measure. Instead, the appropriate definition depends on the comparison being made and the desired treatment of the bond’s cash…
The document explains how to price a European call under Merton’s jump-diffusion model. A Black-Scholes calculation conditioned on a fixed number of jumps is only one component of the price; the full value averages those conditional prices across all…
The document outlines a simple Monte Carlo approach to valuing the wildcard option in Treasury futures. It proposes sampling late-day changes in the cheapest-to-deliver bond during the delivery period, then evaluating each day whether exercising the wildcard…
The document considers how to estimate an option’s implied volatility at a target maturity using options observed at nearby expiries. Its response recommends estimating an at-the-money volatility term structure rather than holding an arbitrary strike fixed…
The discussion asks how to change from a physical probability measure to a risk-neutral measure when an asset follows an additive-noise Ornstein–Uhlenbeck-style process. It distinguishes this specification from geometric Brownian motion, where the diffusion…
This discussion considers whether quasi-Monte Carlo (QMC) can help price path-dependent derivatives and how to speed up Monte Carlo simulations. It explains that an option price is an expectation over risk-neutral paths, so QMC can in principle be used to…
The document explains why an equity index futures price can be below the expected future level of the index. Under the stated setup, the expected index value reflects investors’ required expected return, while the futures price reflects the risk-free rate…
The document explains how an at-market overnight index swap fixed rate is chosen so the swap has zero value at inception. Its floating leg compounds daily overnight rates, while the fixed leg pays the agreed rate according to the contract schedule. Under the…
The discussion contrasts European call and put prices as maturity changes. It gives an arbitrage argument that, under a positive interest rate, a call with a longer maturity cannot be cheaper than an otherwise identical shorter-dated call: if it were, buying…
The document explains the rate-unit convention for fitting Nelson–Siegel–Svensson curves to spot, forward, or discount rates. Its answer states that rates should be entered as decimals, such as 0.05 for a quoted five percent, rather than as whole percentage…
The document clarifies a distributional result for the Cox–Ingersoll–Ross short-rate model. Conditional on the current rate, a scaled future rate has a noncentral chi-square distribution; the rate by itself is not generally described by that same…
The document derives the fixed rate that makes the present values of a swap’s fixed and floating legs equal under a single-curve framework. It first expresses each leg as a discounted sum of accrual-period cash flows, then solves for the fixed rate as the…
The document lays out a broad study checklist for financial risk management. Its product areas include fixed income, equities, currencies, commodities, exotics, and credit derivatives. The concepts span risk and return, hedging, risk neutrality, no-arbitrage…
The document asks what options are represented by root symbols that begin with a digit and end with a stock ticker, using an adjusted-options example in which a root differs from the underlying ticker. The answer identifies these series as Flex options. Flex…