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 the shape of a down-and-in call's value as spot moves around a lower barrier. At high spot levels, the chance of touching the barrier is small, so the option is worth little. As spot approaches the barrier, the probability of activation…
The answer explains stochastic local volatility (SLV) as a hybrid that combines a local volatility surface calibrated to vanilla options with a stochastic process for volatility. The local component helps fit vanilla prices, while the stochastic component…
The document asks why a call option’s theta in the Black–Scholes model does not appear to include a term involving the time change in the underlying share price. It presents the familiar call pricing expression and a standard theta formula, then questions…
The document explains how to invert a two-way FX forward quote when changing the currency pair’s direction. Its example asks whether the reciprocal of the EURUSD bid and offer gives the corresponding USDEUR market. The answer confirms inversion, with the…
The document asks why a GBP bond’s spread over gilts differs from the spread implied when converting its funding into USD through a cross-currency swap. It gives an example involving a seven-year bullet bond, a Bloomberg-derived USD equivalent, and the…
The document sets up a call option on a defaultable bond under a risk-neutral measure. Both the risk-free interest rate and the default hazard rate follow mean-reverting stochastic processes. The option payoff is conditional on the issuer surviving to the…
The response derives a pricing relationship between a call option on an exchange rate and a put option on the inverse exchange rate. It defines the rate as domestic currency per unit of foreign currency, then rewrites the call payoff using the reciprocal…
The document discusses whether the perpetual American put, a standard Black–Scholes example with an optimal lower exercise barrier, conflicts with the model’s assumptions because hedging may require a stock short held indefinitely. One answer focuses on…
The document asks for approachable introductions to non-constant volatility models, including CEV, Heston, and SABR, after finding a more advanced volatility-surface text too demanding. The replies recommend resources at different levels and scopes rather…
The document poses an interview problem for estimating the expectation of a payoff at a future time when the underlying follows a diffusion whose volatility depends on its current value. It asks for two approximate algorithms: a stochastic simulation and a…
The document asks how Bloomberg calculates implied volatility smiles for equities and mentions a possible lognormal-mixture model for stock prices. The replies point readers to Bloomberg’s BVOL equity implied volatility calculations paper as the available…
The document asks whether a forward rate curve can be used to infer SABR parameters, with beta excluded, and then price derivatives. The accepted reply explains that the forward describes the underlying rate process, while SABR also models stochastic…
The document explains why a currency swap’s future payments are valued by discounting them at current market yields. Under annual compounding, a future cash flow is converted to present value by dividing by one plus the relevant yield raised to the time…
The document explains two related ideas for European options settled in bitcoin: put-call parity for identifying a conversion or reversion mispricing, and delta hedging to manage exposure to the underlying. For matching calls and puts, parity relates their…
The document derives the interest-rate duration of a zero-coupon bond under continuous compounding. Its price at time t for maturity T is represented by discounting the single payment at rate r. Duration is defined as the negative derivative of price with…
The document discusses how to hedge a long American put in a two-period binomial stock and cash market while repaying a loan used to buy the option. The central method is dynamic replication: calculate the option's stock hedge at each node, then rebalance as…
Financial models serve several purposes: forecasting selected quantities, pricing instruments relative to market quotes, describing economic relationships, and helping investors make decisions under uncertainty. A volatility model such as GARCH can use…
The document discusses simulating the value and risk of a portfolio holding FX forwards across currencies and maturities. It distinguishes risk measurement from pricing: one answer says vanilla forwards can be valued directly, while Monte Carlo may be…
The document describes using QuantLib’s SABR swaption volatility cube with an at-the-money volatility matrix, strike spreads, volatility spreads, and SABR parameter vectors. It discusses calibrating normal at-the-money volatility by fixing beta at zero and…
The document asks how to approximate a function from values observed at a finite set of points using a weighted sum of call-like payoff functions at selected strikes. It frames the goal as a super-replication problem: find coefficients so that the…
The document presents a negative basis trade example that compares a bond’s Z-spread with the cost of repo funding and CDS protection. It gives a Z-spread of 100 basis points, a CDS spread of 40 basis points, and repo funding at 2%, described as Libor plus…
The document addresses why a drift adjustment may appear unnecessary when changing from the money-market account numeraire to a zero-coupon bond maturing at the payoff date. It defines the money-market account and bond price, then shows that with…
The document discusses implied-volatility calculations from option-chain prices and spot values sampled at potentially different times. Its example shows a call quote below its discounted intrinsic value, so the inputs violate the no-arbitrage lower bound…
The document raises foundational questions about pricing a call or put in a two-state binomial model. The method described is replication: combine positions whose payoffs match the option's payoff in each possible future state, then infer the option value…