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20,364 dokumenter
The document explains why a Wilshire 5000-to-GDP series built from normalized index values can still be compared over time, and why it should not automatically be read as a literal ratio of market capitalization in dollars to GDP in dollars. The Wilshire…
The document explores how to allocate capital among models that trade different instruments, strategies, and holding periods. One proposed starting point is to treat each strategy–instrument combination as a portfolio component and apply mean–variance…
The document addresses an apparent mismatch between simulated discount factors in a Hull–White one-factor Monte Carlo model and the market discount curve at the initial time. Its central point is that the model’s no-arbitrage setup is intended to reproduce…
The document explains how to construct an equally dollar-weighted portfolio and calculate its periodic returns. The portfolio return at each time step is the arithmetic average of the constituent returns when the portfolio is rebalanced to equal weights.…
The discussion frames hedge selection as choosing weights on available instruments to reduce the combined portfolio’s PnL variance. A simple example shows that when matching instruments exist, the method should recover offsetting positions; with imperfect…
The question examines how to define terminal wealth in a finite-horizon asset-pricing model. Agents have exponential utility and consume only in the final period, so their objective is to maximize wealth at the horizon. Earlier wealth can be described…
The question concerns how to infer an equity’s local volatility when its drift is the short rate and that rate is stochastic. The author proposes adjusting market implied volatility on a forward for short-rate volatility, then asks whether cumulative…
The document explains GSR as the Gaussian Short Rate model and gives its risk-neutral short-rate dynamics in mean-reverting form, with time-varying reversion, level, and volatility. It places GSR within the broader family of affine short-rate models, whose…
The document investigates why changing a Euribor index tenor appears not to alter zero rates built from swap quotes in a QuantLib example. The explanation focuses on single-curve construction: the same curve is used both to estimate floating-leg forwards and…
The document considers how to value currency options when a central bank caps an exchange rate, using the Swiss National Bank’s franc ceiling against the euro as context. Its answer argues that standard models calibrated to historical market behavior may be…
The note examines a claim that pays one dollar when a stock first reaches a specified upper level, under a zero-interest-rate assumption. Although a zero-drift stock model makes the stock price a martingale, equating its initial expected value with its value…
The discussion considers why a multi-period mean-variance portfolio plan can be time-inconsistent: a strategy that maximizes expected terminal wealth subject to a risk penalty today may no longer be optimal when reconsidered at a later date. It asks whether…
The note explains how a finite-difference valuation of an American option should handle a discrete dividend at an ex-dividend date. The stock-price jump is represented by mapping the option value just after the dividend to the value just before it,…
The note clarifies how the continuously compounded yield of a zero-coupon bond relates to its log price. For a bond paying one unit at maturity after n periods, its price is the exponential of minus yield times maturity. Taking logarithms gives log price…
The discussion explains how overnight index swaps and Libor–OIS basis swaps relate to interest-rate curve construction. An OIS floating coupon compounds daily overnight fixings over the accrual period and annualizes the resulting compounded return. A basis…
The discussion considers missing daily prices in a futures portfolio, especially where spread legs become misaligned and create artificial profit and loss. It warns that imputing returns changes the observed distribution and can distort historical value at…
The discussion evaluates a proposed currency index that would weight exchange-rate changes by each currency’s share of daily trading volume. A central obstacle is that spot foreign exchange is mostly traded over the counter, so comprehensive daily volume is…
The document discusses how to feed time series with uneven observation density into a deep learning model, especially when each batch should retain historical context. It argues that the appropriate representation depends on the model and learning method.…
The document asks why a payoff proportional to the stochastic discount factor belongs to the mean–variance frontier. The answer’s intuition is that the payoff and the stochastic discount factor move perfectly together: scaling one by a positive constant does…
The document offers an intuitive explanation for why standard call and put options have positive gamma in the Black–Scholes setting. As the underlying price rises, a call’s delta rises toward one because the option behaves more like the underlying. A put’s…
The document explains why analyzing option Greeks is not expected to improve the payout of a standard box spread. A box combines calls and puts at two strikes to create a payoff similar to a loan or zero-coupon bond. Its return reflects the risk-free rate…
The post works through a derivation of call-option gamma by differentiating an option-price expectation and using the Dirac delta to evaluate the resulting integral. The key step is to recognize the density of the transformed variable as lognormal, apply the…
The discussion examines the value of a total return swap that either party may terminate during a performance period. It contrasts a discounted mark-to-market valuation for a non-cancellable swap with an accrual-style cancellation payoff. One answer argues…
The post asks whether linear interpolation of implied volatility can create arbitrage, distinguishing interpolation across maturities from interpolation across strikes. It notes the concern that interpolating volatility over time may violate calendar…