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 explains why the term risk-neutral probability is used in derivative pricing, even though the measure is not a direct statement of real-world event odds. The question notes that risk attitudes are reflected in the pricing measure and that, under…
The document considers a European call option on the VIX, expressing its payoff as the positive part of the square root of a variable representing squared VIX, minus the strike. It states a Fourier transform involving the error function and asks how that…
The document presents a question about iteratively estimating volatility under the Heston–Nandi model from simulated price data. The author simulates a price process using a separate GARCH-generated volatility series, then applies a proposed recursion to…
The document considers how to add EURUSD European options to a one-day Monte Carlo VaR framework already using correlated historical shocks for FX and commodity returns. The proposed method applies each simulated spot return, reduces time to expiry by one…
The example tests whether a stock, call, and put with the same strike are priced consistently. It proposes buying the put and the stock while selling the call. For the stated prices, the combined position costs less than its payoff at expiration, which the…
The document considers an option that pays one dollar if a non-dividend-paying stock, initially priced at one dollar, reaches an upper barrier. A geometric Brownian motion assumption under risk-neutral pricing gives the questioner a value of the reciprocal…
The document discusses gathering historical listed-option chains and interest-rate inputs for model-free implied-volatility research across several equity indices. It describes using a date override to retrieve historical option tickers for more recent…
The document asks how to estimate the chance that the euro falls below a specified exchange-rate barrier at any point before a deadline. It includes an attempted calculation using an American digital option formula and market inputs such as spot price,…
The document frames a Monte Carlo pricing problem for an option on a range accrual note under a Heath-Jarrow-Morton interest-rate model. It specifies a note with quarterly coupons and a three-year maturity. Coupon amounts are formed from an average of daily…
The document explains why exercising an American call before expiry usually sacrifices value. Before maturity, an in-the-money call generally has time value and is worth at least its immediate exercise payoff. Selling the option can therefore realize more…
This troubleshooting account describes a failed attempt to bootstrap an optionlet volatility surface from cap and floor volatility data with QuantLibXL. The failure appeared during optionlet volatility calculation, with a root search unable to bracket a…
The discussion explains how to model portfolios whose returns are bounded on one side, using long vanilla options as the example. Rather than fitting a symmetric distribution directly to option returns, it models the underlying stock price and, where…
The document shows how to value a stock-contingent payoff that pays one cash amount when the terminal stock price lies between two thresholds, a larger amount above the upper threshold, and nothing below the lower threshold. The key construction is to…
The document examines why practitioners may price options on futures under a forward measure when a risk-neutral measure is also available. The accepted reply distinguishes futures from forwards: futures prices are martingales under the risk-neutral measure…
The document discusses power reverse dual-currency notes through a Yen investor’s exposure to a Brazilian real and Yen-linked payoff. One explanation frames the investor as long the real forward, or equivalently as holding exposure to the real spot and a…
The document asks whether a callable bond can be valued as a straight bond minus a call option on that bond. It also asks whether the difference between the straight bond's value and the callable bond's value equals a receiver swaption, based on the proposed…
The question proposes estimating aggregate market-maker profit from quoted spreads multiplied by traded quantity in highly liquid options data. The response explains why this spread-based calculation is incomplete: it does not capture losses or gains from…
The document asks whether a principal-protected note can be replicated with a call option and a strip bond while delivering a specified share of an index return, subject to a maximum return. The response suggests that the note’s participation depends on how…
The document gives a basic historical method for estimating volatility from a time series of observed prices. Calculate consecutive log returns as the natural logarithm of each price divided by the previous price, then take the standard deviation of those…
The document explains how to price a European put in a two-period stock tree when the risk-free rate is zero. It questions a proposed formula with binomial probabilities and instead outlines replication: construct a stock-and-cash portfolio that matches the…
The note explains why an out-of-the-money binary call price need not rise monotonically with implied volatility. It suggests plotting the option price across increasing volatility values and gives an example with spot just below the strike, zero interest…
The document explains an equity-linked principal-protected note whose payoff adds the index’s absolute return only if the index stays within a specified barrier throughout the observation period. Crossing the barrier removes the gain, while principal is…
The question compares broker-displayed theta for SPX index options and E-mini futures options with similar strikes and nearby expiries. Their quoted option prices are close, yet the reported theta differs, prompting a question about whether European versus…
The document examines how a one-factor mean-reverting stochastic volatility model for instantaneous forward variance might extend to several factors. It describes a lognormal variance process driven by a mean-reverting Ornstein–Uhlenbeck factor, with the…