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.
8,116 documents
The document presents a QuantLib Python calibration attempt for a time dependent Heston model that fails with a Boost assertion. The code builds a volatility surface, creates a piecewise time dependent model, attaches an analytic pricing engine, and…
The document discusses why an online broker may cap the number of legs in a single options spread order. Its main explanation is that brokers submit orders using structures recognized by options exchanges, and the permitted order formats and applicable rules…
Liquidity depends on the asset class and on how participants access each market. The document compares spot, futures, options, and swaps across currencies, single stocks, equity indices, commodities, and fixed income. It offers a practical framework: there…
The document considers whether an equity option’s implied volatility should be adjusted when the underlying price moves. It describes alternative ways to hold the volatility surface fixed: sticky strike keeps implied volatility tied to each strike, while…
The document explains how the Cox–Ross–Rubinstein binomial option-pricing recursion approaches the Black–Scholes model as the time step shrinks. It corrects the risk-neutral pricing equation, then uses first-order expansions of the up and down moves and the…
The document examines implausible risk-free rates inferred by regressing option collars on SPX options close to expiration. It explains that put-call parity calculations can become distorted when options and their underlying continue trading on different…
The document addresses a numerical implementation issue in the CGMY model’s characteristic function. The questioner encounters an error because the expression includes gamma functions evaluated at negative values and asks whether the formula is incorrect.…
This beginner discussion distinguishes an option’s payoff at expiration from its value before expiration. Changing volatility does not alter the European option’s terminal payoff diagram; it changes the premium beforehand by changing the range of possible…
The response explains how to handle a gap call, whose strike determining exercise differs from the strike used to calculate the payoff. It rewrites the payoff as the underlying asset paid only when the exercise threshold is crossed, less a fixed amount paid…
The document explains the basic valuation framework for residential and commercial mortgage-backed securities: estimate the security’s cash flows and discount them to calculate present value. The central difficulty is forecasting those cash flows, especially…
The document addresses Monte Carlo valuation of a call option on a zero-coupon bond under the Vasicek short-rate model. It first challenges the question’s stated closed-form benchmark, deriving a bond-option price using the Vasicek bond pricing function and…
The document addresses the misconception that volatility is bounded by the largest possible percentage decline in a stock price. In the Black–Scholes framework, volatility scales the standard deviation of the asset’s log return over the option’s life. That…
The document explains why expected value differs for holding an underlying asset and holding a call option. An underlying position is exposed to the asset’s full range of possible prices, so its expected price weights every outcome by its probability. A…
The document asks why a Black–Scholes option price differs from an expected option payoff calculated from a spreadsheet model. One response identifies a key model mismatch: Black–Scholes assumes lognormal stock prices, while the spreadsheet uses normally…
The discussion points to two practical approaches for hedging volatility swaps. For forward-starting swaps, it cites a method that uses straddles at a particular strike, with hedge notional linked to the volatility skew at that strike. For…
The document considers valuing a European call when its underlying asset cannot be traded, so the continuous-trading replication assumptions behind Black–Scholes are unavailable. Suggested inputs and approaches include estimating the underlying’s value from…
The document contrasts implied volatility from near-expiry, at-the-money S&P 500 options with the VIX. The response characterizes VIX as a discrete approximation to the square root of a theoretical fair variance swap strike, with its calculation window set…
The document considers a long call calendar spread when the underlying rises above the shared strike by the short option's expiration. It asks whether the spread necessarily loses its entire opening debit, using an example in which the near-dated call is…
The discussion explains how to interpret and scale Greeks for a GBP/USD call option. It emphasizes that the currency pair’s quotation and the chosen risk convention affect the sign and currency value of delta. A trader described as hedged by 50 deltas holds…
The document addresses numerical instability when a finite-difference method prices a call option using its terminal payoff, which has a kink at the strike. Near that point, a coarse grid can make a central approximation to the second derivative very large,…
The document asks how to compute higher moments of the time integral of an exponential Brownian motion, a quantity relevant to arithmetic Asian options. It first gives the expected value, then presents a general expression for the m-th moment using divided…
The document describes a QuantLib calibration problem for the G2++ interest-rate model in a negative-rate environment. The reported error arises because the cap helper uses shifted lognormal volatility with zero displacement, which requires the strike plus…
The document explains when European calls and puts with the same strike and maturity should have matching implied volatilities. Under put-call parity, their implied volatilities coincide at the at-the-money forward strike when the other pricing inputs are…
The document shows how to price a payoff of the form (S_T f(S_T))^+ by changing from the money-market numeraire to the stock numeraire. Starting with a risk-neutral geometric Brownian motion, it defines the new measure using the discounted stock as the…