คลังความรู้

The document explains why a fund that specializes in market making may later operate as an independent business. It identifies Citadel as an example of a firm engaged in market making and describes the activity as potentially profitable on a risk-adjusted…

The document proposes a cash-flow accounting framework for the stock market. It lists investors and institutions as sources of investment capital, and dividends, acquisitions, and buybacks as flows back toward shareholders. It places IPO proceeds, share…

The document examines the assumption that a small order has negligible influence on market observations and price dynamics. That assumption can make historical backtests easier because the recorded order book or other market data are left unchanged by…

The document explains a measure change used in a derivation of constant-maturity swap convexity. It considers the expectation of a swap rate under a forward measure associated with a bond maturing at the payment date, then rewrites it under an annuity…

The document raises questions about whether risk of ruin (ROR), a concept associated with gambling, can describe trading losses and whether a zero probability in a published table means ruin is impossible or merely very unlikely. It also asks how win rate…

The document asks how to interpret a VaR estimate for extreme positive returns after using extreme value theory to model both negative and positive tails. The response distinguishes downside risk from the upper tail: when losses correspond to negative…

The document examines how quarterly excess returns on Treasury bills and long-term bonds are calculated in an appendix to a 1988 asset-pricing paper. It describes the maturities involved and asks how the paper’s formulas relate to a direct holding-period…

The document asks how sums of squared log returns can approximate integrated variance, and why the approximation works even when returns are sampled daily. It distinguishes realized variance, formed by summing squared returns over a sampling grid, from…

The document frames a regulatory validation problem: when a bank using the internal ratings based approach acquires another bank’s loan portfolio, how can it show that its existing probability of default model and risk classes are suitable for the new…

The document asks whether the US government follows a money-printing policy, how such a policy might be measured, and what drives persistent inflation. The response suggests looking at the monetary base as a measure of currency and bank reserves in…

The document explains why an institutional customer might use an executing broker even when it already has a prime brokerage relationship. Prime brokers provide a broader package of services and can execute trades, while executing brokers may focus on…

The document contrasts two mathematical characterizations of the perpetual American put discussed in a stochastic calculus text. The analytical treatment describes the option value through partial differential inequalities and linear complementary…

This question describes a Monte Carlo implementation of the Libor Market Model (LMM) for simulating forward rates before a swaption’s exercise date. The model uses an initial forward curve, a correlation matrix, and time-dependent volatilities, with…

The document proposes a staged way to learn Monte Carlo methods, while emphasizing that the right material depends on the problem. It starts with simple simulations such as dice, coin tosses, estimating areas, and pricing a vanilla option. It recommends…

The document concerns Monte Carlo valuation of a barrier option when the underlying follows a jump-diffusion process. The question reports a simulated value that differs from the cited paper and jump probabilities that sometimes fall outside the valid…

The document diagnoses a QuantLib error raised while building a Black variance surface from option implied volatilities. The reported validation requires expiry dates to be unique and arranged in chronological order. In the supplied schedule, one-year expiry…

For standard European calls and puts, the document explains why a higher ask price usually implies a higher ask implied volatility than bid implied volatility. The key link is that, holding other inputs constant, these option prices increase as volatility…

The document asks whether a derivative can have a payoff that is quadratic in the underlying asset’s price, including a version floored at zero. The responses explain that a bespoke payoff could be requested from a bank, while emphasizing that the buyer…

The document explains why interest deductibility is called a tax shield and how it affects the after-tax cost of debt used in weighted average cost of capital. Its central distinction is between a firm’s lower tax bill and its overall profit: debt creates…

The document considers simulating a process formed by adding Brownian motion to a compound Poisson jump process. Its example generates Gaussian Brownian increments with standard deviation scaled by the square root of the time step, then adds potential…

The document asks whether European call prices at a single maturity uniquely determine a time-independent local-volatility function, given that Dupire’s formula ordinarily uses a surface across maturities. One answer cites a result establishing a unique…

The document distinguishes the risk-reversal trading strategy from the market convention used to quote a risk reversal on a volatility surface. A risk reversal combines a call and a put, often selected at specified delta points, while the quotation…

The document explains why the stock price and the value of interest-bearing cash satisfy the Black–Scholes pricing PDE. The stock itself is a traded asset whose value is the underlying price, while a bank balance grows deterministically at the risk-free…

The document compares the spot sensitivities of American and European calls when the stock pays a single dividend before expiry and interest rates are zero. It represents the American call as the expected value of the better choice at the dividend date:…