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เอกสาร 20,364 รายการ
The note gives a rough way to estimate daily value at risk for a corporate bond position using its CS01, the change in value for a one basis point move in credit spread. It suggests estimating a high-quantile spread move from historical data or a Monte Carlo…
The document explains how a Monte Carlo simulation can align with Black 76 without first converting futures prices into spot prices. It starts from a lognormal spot-price process with drift and volatility, then substitutes the spot-forward relationship so…
The document explains that a numeraire used for pricing does not always need to be a traded asset. It presents the risk neutral pricing relation under a measure associated with the chosen numeraire, then describes expressing derivative and underlying prices…
The document asks whether the publication of the Black–Scholes option-pricing paper in 1973 was directly connected to the founding and launch of the Chicago Board Options Exchange that year. The cited historical account says the formula was not developed to…
The document explains how to price a claim paying the cosine of a terminal stock price under risk-neutral pricing when the stock follows geometric Brownian motion. It writes the discounted expected payoff as an integral over the risk-neutral lognormal…
The document considers whether maximum likelihood and ordinary least squares estimates coincide for an autoregressive process, focusing on the role of Gaussian errors. Its answer uses an AR(1) illustration that can be extended conceptually to AR(2). Although…
The document explains why the linear-exponential (Linex) loss function converges to squared-error loss as its asymmetry parameter approaches zero. It considers a forecast error and expands the exponential term in the Linex formula as a Maclaurin series. The…
The document asks why a portfolio might impose dollar neutrality in addition to beta neutrality. Beta neutrality constrains estimated market exposure, while dollar neutrality balances total long and short weights. The answer illustrates that a beta-neutral…
The document considers how often and how heavily to trade a favorable card-drawing wager when capital is finite. It distinguishes the decision to accept a positive-expectation trade from sizing repeated bets, and presents expected utility as a way to…
The document explains the combined payoff of a long up-and-in put and a short up-and-in call with the same strike, maturity, and barrier. If the underlying reaches the barrier before expiry, both options activate and behave like vanilla options. Put-call…
The document asks how to calculate 95% Value at Risk from simulated portfolio losses sorted in ascending order. It proposes taking the 5th percentile and questions whether this selects the correct side, since the resulting figure is below the mean. The…
The document considers the impact of replacing established overnight discount rates with new risk-free rates on uncleared swaptions. It asks whether valuation changes should be compensated, distinguishing temporary changes in a swap’s discounted value from…
The document explores how a forward interest rate follows from the prices of zero-coupon bonds with different maturities. It proposes holding a long position in the longer-maturity bond and a short position in a scaled amount of the shorter-maturity bond,…
The document explains replication as matching a derivative’s payoff across every possible model state using positions in the underlying stock and a money market account. In a one-period example, stock and bond holdings are chosen so their combined terminal…
The document asks whether financial institutions use GARCH models in risk systems that calculate expected shortfall. It cites a practical primer by an author whose listed affiliations include a bank, as an example of practitioner-oriented discussion. The…
The document considers whether linear hedges, such as delta hedges, can meet most clients' needs without other derivatives. It notes that Black–Scholes theory can use a rebalanced linear hedge to replicate a nonlinear option payoff. For linear exposures, or…
The document explains why option traders sometimes treat theta as a proxy for gamma, focusing on a delta-neutral portfolio. It uses the Black–Scholes differential equation to relate portfolio time decay, delta, gamma, interest rates, and the underlying…
The document asks where to obtain price levels for the CRSP value-weighted index that exclude distributions. The author can access WRDS index returns, total market value, and market value of securities used, but reports that returns computed from the latter…
The document explains Trade-at-Settlement orders in futures markets. A TAS trade sets the transaction price relative to the eventual futures settlement price, with the chosen offset recorded in the TAS order book. The reply characterizes the trade as an…
The document considers how to estimate a portfolio’s return distribution for an expected shortfall constraint when only a limited history of asset returns is available. It questions whether a normal approximation based on the central limit theorem is…
The document addresses how to find long historical series of nonfinancial measurements for testing correlations with a financial analysis or trading algorithm. It suggests looking at unusual public datasets and gives examples of possible sources, including…
The document examines the Black–Scholes risk-neutral drift relation and asks whether its negative volatility adjustment conflicts with the observation that higher interest rates can coincide with falling stock prices. The replies explain that the relation…
The document asks whether an implied volatility surface can be used to calculate options strategy P&L and variance swap P&L when individual option prices are unavailable. The response says a surface can support these calculations if its construction…
The document describes a Monte Carlo setup for a correlation swap: pairs of normally distributed asset returns are generated with a specified population correlation, and sample correlation is calculated across observation periods for each simulated path. The…