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 derives a local delta-gamma hedge for a target option using a second option and the underlying asset. It writes the hedge as a combination of the underlying and the second option, then matches the target option's gamma by setting the second…
The discussion distinguishes a linearly interpolated swaption volatility cube from a cube generated using SABR. Linear interpolation of market quotes can describe a static set of Black-model volatilities across strikes and maturities. SABR instead models…
The discussion asks why some state-contingent prices in an example from Ross's Recovery Theorem exceed one. A response offers an intuition: a guaranteed payment in a particular future state can be highly valuable when that state involves catastrophe or when…
The document presents several ways to estimate theoretical option prices when a new underlying has little or no options-market history. As a basic starting point, it suggests using historical return volatility as a constant volatility for near-the-money…
The document asks how to calculate a bond price at a future simulation time using forward rates produced by the HJM procedure described in Glasserman. It proposes discounting across the remaining grid intervals by summing the simulated forward rates for that…
The document asks how to interpret the payoff of a European floating-strike lookback call. It describes the strike as the maximum stock price reached over the option’s life and questions whether the payoff must therefore be zero or negative at maturity. This…
The document derives the probability that a geometric Brownian motion stays below a barrier over a time interval, conditional on its terminal price. A direct Brownian-bridge formula seems tempting after taking logarithms, but the resulting Brownian-motion…
The document explains how interest rate swaps (IRS) and overnight indexed swaps (OIS) differ in access and hedging use. Counterparty type does not by itself limit access to OIS: a corporate with an ISDA agreement to trade IRS with a bank can generally trade…
The note explains how to choose volatility-surface inputs when calibrating a model for autocallable products. Its central recommendation is to calibrate one model to the autocalls held in the portfolio, reflecting that hedging is generally managed at…
The document derives a Fourier representation for pricing a European option under risk-neutral valuation. It identifies the payoff as a function of terminal log price and explains why a call payoff does not have a conventional Fourier transform: it grows…
The document raises a currency-convention question about the delta of a USD-denominated USDJPY option when the holder measures value in another currency. It distinguishes the option’s sensitivity to USDJPY spot, expressed as the derivative of its dollar…
The document asks about emerging-market currency bonds priced using cross-currency swap rates and about the participants and drivers of fixed-local-currency versus floating-dollar swaps. The response describes these swaps as longer-dated expressions of…
The document concerns a pricing partial differential equation for a derivative whose underlying variable is an interest rate. Its general specification uses drift and volatility functions of time and the short rate, together with a market price of risk. The…
The document considers a fund guarantee that pays the customer the greater of the initial investment or the fee-adjusted fund value at maturity. The answer rewrites the payoff as the initial amount plus a call option on the fund, with a strike increased to…
The document explores how a Black–Scholes-style option equation changes when the hedged portfolio is assumed to have its own stochastic diffusion. Starting with geometric Brownian motion for the underlying, it applies Itô’s lemma to the option value and…
The document asks how the conditional-expectation change-of-measure identity relates to the unconditional formula. For equivalent measures P and Q with Radon–Nikodym density dQ/dP, it recalls that an expectation under Q can be written as a P expectation…
The document explains how to interpret opposite moves in implied volatility for options expiring on adjacent dates. It emphasizes that implied total variance, rather than implied volatility alone, is the quantity to compare across expirations. Total variance…
The document clarifies that reference rates used for swap floating legs and rates used to discount cash flows are distinct choices. It notes that EURIBOR remained in use, while EONIA was replaced by €STR, and that USD markets used both Federal Funds and SOFR…
An overnight index swap curve is a term structure built from market instruments referencing an overnight rate. The answer explains that curve construction uses instruments such as futures and swaps across maturities to infer discount factors and forward…
The document asks whether vanilla options at two maturities can replicate a payoff based on the ratio of an underlying’s later value to its earlier value. The response identifies the contract as a forward-starting option and explains why prices of ordinary…
The document examines how to derive the differential of a time-dependent integral of a stochastic process, and asks about the correct integration variable in the expression. One response approximates the integral with sums over a partition, applies Itô's…
The document asks how the annuity should enter swaption risk calculations when a swaption price is expressed as the annuity multiplied by a Black-model price. It focuses on whether the annuity can be treated as fixed when calculating delta, and whether…
The document raises a practical question about estimating value at risk for a portfolio of options. Its proposed approach is to simulate future underlying prices, revalue the options theoretically at each simulated price, and examine the resulting…
The document presents a historical index-option example in which a European call near the money has positive reported theta. The author uses the observed discount factor to infer a negative risk-free rate, then uses spot, forward, and maturity to infer a…