নলেজ লাইব্রেরি

The document explains how to obtain the dynamics of a zero-coupon bond price from a stochastic model for the short rate. Under the risk-neutral measure, the bond price is expressed as the expected discount factor from the current time to maturity. Assuming…

The document asks whether floating rate notes have no roll-down over a given horizon because they are relatively insulated from interest rate risk. The response distinguishes pure floaters from notes that pay a margin over the reference rate. For a pure…

The document raises a fixed income question about callable perpetual bonds. It observes that Bloomberg’s calculated yield uses the first call date as the workout date, and that for a fixed price this date appears to produce the lowest yield among the…

The document considers the risks created when hedging a TRY/JPY call option with positions in other currency pairs. One answer observes that expressing the hedge through several currency spots introduces exposure to multiple currencies, and that the original…

The document explains why overnight indexed swap rates became a common discount curve for collateralized derivatives. In the US example, OIS reflects expectations for the Fed Funds rate, which monetary policy influences, while private interbank funding rates…

The document presents an APGARCH model output with a negative estimate for gamma and asks what its sign means and whether it indicates a leverage effect. The table also reports the estimate’s standard error, test statistic, and p-value, alongside estimates…

This note explains how to read a historical Value at Risk estimate from a sorted sample of profit and loss outcomes. For a stated confidence level, the relevant tail observation is selected from the loss end of the distribution; gains do not become VaR…

This note compares approaches for fitting European call prices across strike and recovering the risk-neutral distribution implied by options. One method fits call prices directly with arbitrage-constrained cubic smoothing splines; the second derivative of…

This note explains two assumptions desks use to update an implied volatility surface between full calibrations. Under sticky strike, implied volatility stays fixed for each strike as the underlying price changes. An option at a given strike is therefore…

The document asks why a swap’s annuity factor should be proportional to its coupon value change for a one basis point move, called CV01. It starts from the par swap pricing equation, expressing the fixed coupon and discount-factor sum alongside the maturity…

The document asks how to compare company performance while reducing the influence of macroeconomic changes such as interest rates, crises, and inflation. It also raises the idea of expressing company financial metrics relative to other companies instead of…

The document explains how to select curves for valuing interest rate swaps and swaptions when floating indices have different tenors, such as three or six months. The curve associated with the floating index is used to forecast its cash flows: a swap…

The document discusses how to compare Vasicek and Cox–Ingersoll–Ross (CIR) models for fitting zero-rate curves. Rather than judging the models from a single observed curve, it recommends calibrating each across many curves with varied shapes, including flat,…

The document asks why a 14-period RSI calculated from daily closes differs from an hourly RSI over the same calendar span, even when the hourly period is scaled to 98 bars. It compares roughly 230 daily observations with about 1,500 hourly observations for…

This note discusses how point-in-time (PIT) and through-the-cycle (TTC) default probabilities fit into a one-factor Merton-style credit model. It presents the conditional default probability given a systemic economic factor and explains that inserting a TTC…

This introductory explanation clarifies the meaning and timing of an option premium and distinguishes exercise rules by option style. In the example, the quoted trading price of a call is its premium: the buyer pays that amount when entering the option…

This note contrasts the analytical minimum-variance portfolio with portfolio optimization for maximum skewness. The minimum-variance problem has a closed-form solution under a full-investment constraint. The skewness objective instead depends on a coskewness…

This note explains one implementation’s method for choosing the initial Parabolic SAR value when calculating the indicator from FX price data. It uses the first two bars’ highs to infer the initial direction: when the first high is below the second, it…

The document discusses how to align an expert-based internal scorecard for commercial loans with external agency rating categories. It suggests ordinal logistic regression when agency rating category is the target, since ratings are ordered categories rather…

The document asks why stochastic-volatility modeling often introduces a market price of risk when option pricing can begin directly under a risk-neutral measure. It describes a traditional setup in which variance has historical dynamics, its drift changes…

The document presents a question about a European call priced below its put-call parity lower bound. In the example, an arbitrageur shorts stock, buys the underpriced call, and invests the cash proceeds. At expiry, if the stock is above the strike,…

The document offers two practical ways to build intuition about whether an option’s volatility skew is unusually cheap or expensive. One approach is to consider how realized volatility might differ when the underlying is near a particular strike. If…

The document explains why making a discounted dividend-paying stock price a martingale under a chosen probability measure does not, by itself, justify risk-neutral pricing. The key condition concerns discounted values of self-financing portfolios. Holding a…

A bond that trades special in the repo market can be financed at a rate below general collateral (GC). That financing advantage can support a higher bond price, or equivalently a lower yield, than would prevail without specialness. The document estimates the…