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20,364 dokumenter
The document works through a question about deriving a continuous-time equation for the value of an investment with an option to stop. It presents a Bellman relation that compares immediate stopping value with the value of continuing, including profit flow…
The document asks how to check a Python implementation of delta hedging for a short European call, offset by a long position in the stock sized to the option’s delta. It proposes examining the distribution of the combined hedge-and-option profit and loss…
The document raises a calibration problem for classical short-rate models, including Black-Karasinski and Hull-White, during the sharp rate increases of 2022–2023. The author is concerned that model parameters may struggle to fit current rate levels while…
Volume time rescales a trading day according to cumulative traded volume, with the measure progressing from the session open to its close. Because activity varies across the day, this clock can make an individual instrument’s observations more regular in…
The note addresses how to obtain zero rates for corporate bond cash flow mapping. It recommends building a yield curve by bootstrapping from liquid market instruments, such as deposits, swaps, or futures, and then using the resulting curve for discounting.…
The note asks whether a forward price equals a futures price when the contracts share a maturity and the market has no dividends, constant interest rates, and no arbitrage. The answer derives the standard cost-of-carry relationship: the delivery price is…
The document asks how to interpolate implied volatility between listed maturities to construct a volatility surface for a Black–Scholes delta-hedging experiment. It considers bilinear interpolation and seeks guidance on methods that can fill values between…
The document clarifies how a bond futures conversion factor relates the futures price to the cheapest-to-deliver bond at delivery. When the delivery basis has converged, the futures price at delivery equals the CTD bond price divided by its conversion…
The document explains how to express a view that an option volatility skew is too flat or too steep while limiting exposure to the overall volatility level. Since option prices move with implied volatility, a trader can combine options at different strikes…
The document presents a bilateral equity option contract with American exercise, linked exercise between parties, post-exercise VWAP averaging, dividend-related strike reductions, and an additional premium tied to rates and the remaining call notional. It…
The discussion addresses why an at-the-money call can appear to have a delta near one when volatility is close to zero. One reply offers an intuition based on positive carry: with a risk-free rate above the dividend yield, a spot-at-the-money option can be…
The document considers how to define quantitative finance and whether finance belongs primarily to mathematics or economics. One proposed definition treats quantitative finance as applied mathematics drawing on statistics, economics, econometrics, game…
A European put with strike K pays no more than K at maturity, since its payoff is the greater of K minus the underlying price and zero. The document applies the no-arbitrage principle: the put cannot be worth more before maturity than a zero-coupon bond…
The document explains why rows generated from a Sobol sequence repeat when the generator is reinitialized inside each asset loop. The generator should persist across draws, and its dimension should match the number of random coordinates needed for one…
The document presents a Python implementation of Longstaff–Schwartz least-squares Monte Carlo for an American-style Asian call with exercise available at discrete dates. The payoff depends on the average underlying price observed up to exercise. The reported…
The document discusses calculating daily log returns from price series with missing observations, where dropping every row containing a missing value can discard too much data. It presents a missing-data convention attributed to CRSP: keep the return missing…
The document examines a portfolio problem that seeks to maximize variance while requiring zero exposure to each listed risk factor. It explains why those constraints alone do not produce a finite maximum: if a feasible portfolio exists, scaling all its…
The document asks how to assess a company’s ability to repay long-term debt within roughly four years, using a book’s screening rule for financially strong businesses. It proposes dividing long-term debt by net income and gives Coca-Cola figures as an…
The document explains why option volatility surfaces may use forward moneyness instead of raw strike. Moneyness measures a strike’s distance from a reference price; forward moneyness compares the strike with the forward price for that option’s maturity. This…
The document compares holding a cryptocurrency investment for a fixed period with periodically withdrawing gains while restoring the original principal. It describes a Monte Carlo example using simulated daily returns, then reports average outcomes for both…
The document suggests replacing normally distributed log returns with Student’s t-distributed returns to model fatter tails in a portfolio growth simulation. The degrees of freedom control tail thickness: lower values produce heavier tails, while increasing…
The document defines rolling for credit default swap contracts, distinguishing the creation of a new series from the maturity of an existing contract. For CDS indices, a new series is introduced on semiannual dates, and its basket of reference entities may…
The document surveys several free or low-cost sources mentioned for historical market data. Its main example is an undocumented onvista interface for retrieving stock tick data by security identifier, exchange, and trading day. The author describes how a…
The document explains two ways to create forward scenarios for a bond yield series. One approach resamples historical yield changes: repeatedly draw changes from the observed series, accumulate them from the latest yield, and use the resulting paths to…