নলেজ লাইব্রেরি

The document poses a question about the conditional expectation of stock returns in a model with a return driver, a volatility term, and an ARCH(1) variance process. The innovation is written as conditional volatility multiplied by a standard normal shock.…

The document discusses simulating returns without assuming a fixed unconditional distribution. It warns that financial returns have time-varying conditional moments, especially persistent volatility clustering, so resampling the unconditional return…

The document clarifies a common backtesting problem in a model that uses a completed candle’s closing price to generate a signal for the next period. The training setup is not automatically biased merely because it predicts a future value from past…

The document considers why a long 7Y1Y payer swaption might show gamma with different signs at the 7-year and 8-year points on a par yield curve. The answer suggests that the reported bucketed exposures may come from repricing after a parallel curve bump,…

The document explains two labels that may appear on otherwise similar futures listings: “full” and “only.” The answer interprets them as references to trading sessions. “Full” denotes the broader CME Globex session, while “only” refers to the open-outcry…

The document examines an attempted derivation connecting bond convexity with squared modified duration. It defines modified duration as the negative price sensitivity to yield, scaled by bond value, and convexity as the similarly scaled second derivative.…

The document presents code intended to simulate a GARCH(1,1) process. It updates conditional variance using a constant plus a coefficient on the previous squared return and another on the previous variance, then multiplies the resulting volatility by a…

The answer argues that implied volatility need not be extracted only from the Black–Scholes lognormal model. It describes constructing option valuation formulas under alternative distributions, including log-hyperbolic-secant, log-Cauchy, log-t, and…

The discussion explains why a normal random-walk increment over a time step of length t/n is scaled by the square root of t/n. Each increment can be written as a standard normal random variable multiplied by that scale, so its variance is t/n. For…

The discussion describes how to represent a complex payoff as a weighted combination of simpler instruments, such as the underlying, zero-coupon bonds, calls, and puts. It frames the task as minimizing the difference between the target payoff and the…

The answer distinguishes three CRSP index concepts by construction and purpose. It characterizes the CRSP US Total Market Index as a relatively recent, market-capitalization-weighted index designed to be held by index funds. It contrasts that product with…

The note explains why the Nifty 50 level observed at 3:30 pm may differ from the price used to settle index options on expiry. The answer states that the settlement price is based on a weighted average of prices during the final 30 minutes of the expiry day.…

The document asks how to value a tracker certificate linked to a basket of index futures. It compares this with a proposed approach for an equity-index tracker: project the underlying using a forward curve, then discount using a discount curve. The question…

The note clarifies that a credit default swap (CDS) spread and a bid–ask spread use the word “spread” for different concepts. A CDS spread is described as the cost of credit protection and, in the answer, as the difference between a credit-risky interest…

The discussion compares ways to hold a long-term view on oil: physical storage, futures, oil-company shares, and other instruments. Physical oil requires storage infrastructure, while rolling futures can incur costs or benefit from the shape of the forward…

The question concerns a chart that overlays exchange-rate log differences with a conditional volatility series and observes that the latter is much smaller, despite similar-looking peaks in other examples. The response emphasizes that log returns and…

The discussion distinguishes the role of two conditions used when building a trinomial pricing tree. The conditional expected stock price is set to grow at the risk-free rate under the tree’s transition probabilities. This is the no-arbitrage condition: it…

The discussion examines why a portfolio’s benchmark beta can fall and lose statistical significance when size, value, and momentum factors are added to a regression. In the example, the benchmark-only model reports a larger, significant loading, while the…

The document explains how the Carr-Madan decomposition represents a European payoff as a bond position, a call-minus-put position at a chosen strike, and integrals of puts and calls weighted by the payoff’s second derivative. In a complete market with…

The discussion explains that an issuer can create a contract whose payoff tracks an asset such as gold by promising clients a cash settlement tied to a defined reference price. This is primarily a contractual arrangement. An exchange traded fund, product, or…

The discussion addresses conflicting published tick sizes for Nikkei 225 mini futures. One third-party futures profile lists a ten-point increment, while the exchange’s product page states a five-yen tick worth ¥500 per contract. The accepted answer says the…

The document raises two modeling issues when applying stochastic quanto pricing formulas to crypto futures and perpetual swaps. First, it questions what domestic discount rate to use when the contract is settled in bitcoin, given the absence of a…

The note evaluates whether a bond index price can be approximated by dividing average coupon yield by yield to maturity. It explains that this ratio is appropriate in the limiting case of a bond with infinite maturity, where price is tied to coupon divided…

The note surveys several forms of arbitrage and relative-value trading rather than developing one strategy in depth. Examples include capital-structure and convertible-bond trades, merger and latency arbitrage, ETF and index arbitrage, and relative-value…