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20,364 documente
The document asks whether the fundamental pricing identity for an asset divided by a numeraire remains valid when their values are correlated. The answer explains that correlation does not invalidate the identity: under the measure associated with a strictly…
The document describes an effort to calibrate a simple stochastic volatility model with the Efficient Method of Moments (EMM), as a step toward calibrating Heston parameters from historical equity returns. The author reproduces a SAS example in Python,…
The document presents cost-of-carry relationships for pricing a forward on an asset that pays dividends or another yield. It gives equivalent expressions using a continuous yield or the present value of future cash flows, then states the value formula for a…
The document describes an attempt to reproduce a vendor price for a discrete arithmetic average price Asian call using the Haug, Haug and Margrabe approximation and Curran’s approximation. It lays out the inputs, reports the author’s calculated values and…
The discussion asks whether security prices can be modeled with hyperbolic rather than exponential discounting. It points to academic work examining the asset-pricing consequences: less patient investors may produce lower stock prices and higher interest…
The document examines a practical issue in pairs trading: reversing which security is treated as the dependent variable can change the estimated hedge ratio and produce very different spread values and z-scores. The author illustrates the problem by fitting…
The document compares local volatility, stochastic volatility, and parameterized approaches for representing an implied volatility surface. Implied volatility is a transformed representation of European option prices, and interpolation in volatility space…
The discussion explains why a stochastic discount factor can be written as an affine function of a portfolio return, and how a normalized form relates to the tangency portfolio. In incomplete markets, pricing conditions generally allow multiple SDFs; scaling…
The document considers whether a single-factor Linear Gaussian Model calibrated to coterminal swaptions can price both payer and receiver Bermudan swaptions. The question arises because the two option types have different exercise boundaries and may respond…
The discussion asks whether statistical arbitrage can work in foreign exchange and describes a study of relative-value trading among G10 currencies. The cited approach forms currency pairs from USD crosses, measures their misalignment, and trades when…
The document asks whether one exchange-traded fund can provide exposure to equity markets around the world, rather than tracking a single national index. The answer points to two broad-market products: one tracking the FTSE Global All Cap Index and another…
The document clarifies the relationship between the drift of a price process and the drift of its logarithm under geometric Brownian motion. Starting from a stochastic differential equation for proportional price changes, Itô’s formula gives a log-price…
The document distinguishes the current VIX level from the behavior of VIX as market conditions change. VIX squared corresponds to a variance swap strike, and the answer uses an analogy with a stock whose current price does not depend on its instantaneous…
The document explains why a Black–Scholes European call with an extremely long maturity may be priced close to the current stock price. Under positive growth conditions, the stock is expected to become much larger than the strike over a sufficiently long…
The document considers a cross-currency basis swap and an offsetting hedge booked with different counterparties under different collateral agreements (CSAs). Because one trade is collateralized in euros and the other in dollars, a move in cross-currency…
The document addresses how effective and maturity dates are set for forward-starting interest rate swaps when a forward-period date falls on a non-business day. It distinguishes a swap-dealer convention, which aligns the forward swap with the date schedule…
The document explains how Eurodollar futures can provide a strip of implied forward rates and how those rates can be used to construct a fixed-for-floating interest rate swap rate. For payment dates, the forward floating rates are weighted by discount…
The document examines a Monte Carlo valuation in which a simulated American call on a non-dividend-paying stock is priced slightly below a European call with the same strike and maturity. The example fits a Student t location-scale distribution to historical…
The document clarifies two Moody’s rating-history symbols used for sovereign foreign-currency long-term debt. A “(P)” before a rating denotes a provisional rating. Moody’s may assign one when it expects the rating to become final after receiving…
The document distinguishes two ways to describe an asset’s systematic risk in the CAPM. The quantity formed by multiplying the asset’s volatility by its correlation with the market expresses market-related risk in volatility units. Beta expresses that same…
The document derives an arbitrage-free price for a European call whose underlying is the geometric mean of several stock prices. It assumes each stock follows risk-neutral geometric Brownian motion with a common interest rate, individual volatilities, and…
The document derives how skewness behaves when independent return increments are combined and how a forward-period skew can be recovered from observations over a longer horizon. For two independent, mean-zero increments, variances add and third central…
The discussion considers quasi-random sampling for Monte Carlo valuation of path-dependent interest-rate options, where each simulated path may require many time steps. Its main recommendation is a dimension-ordering approach: use low-discrepancy…
The document outlines symmetric, also called Löwdin, orthogonalization for a set of linearly independent column vectors. Starting from a matrix of vectors, it seeks a transformed basis whose columns are orthonormal. The general transformation is formed from…