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The document asks whether a European option can be priced in a Black–Scholes setting when its payoff depends on a general transformation of the underlying asset. It illustrates the question with a call payoff equal to the positive part of a transformed…
The document poses a numerical modeling question about discretizing a mean reverting Ornstein–Uhlenbeck process that combines continuous Brownian noise with random jumps. The jump component is modeled as a normally distributed jump size multiplied by a…
The document explains why historical value at risk can be unreliable when an asset has only a short return history: the observed sample may not include the full range of plausible losses. It considers using sector returns as a proxy, but notes that averaging…
The document discusses how to interpret and empirically assess Geometric Brownian Motion (GBM). Under GBM, log returns follow a normal distribution whose mean combines the drift and a volatility adjustment. The drift is therefore a model parameter: its…
The document presents practical ways to estimate the parameters of the Vasicek short-rate model without relying only on an unconstrained fit to bond prices. One approach discretizes the model into an approximate AR(1) process and matches theoretical and…
The document explains why daily forex observations cannot be transformed into tick bars or volume bars. Daily prices are aggregates of underlying market activity, so they do not retain the sequence of individual quotes, trades, or trade sizes needed to…
The document explains how TIPS can produce a positive nominal return despite a negative real yield, while still failing to preserve purchasing power. At maturity, inflation adjusts principal, but the adjusted payment may not offset the purchase price; the…
The document explains how to calculate an FX outright forward rate from spot and broker-quoted forward points. The stated calculation is to add the forward points to spot: for the one-month EUR/PLN example, 3.4550 plus 0.0079 gives 3.4629. The question also…
The document asks whether refinancing should be triggered by a simple comparison between lower interest payments and refinancing fees. It presents consumer heuristics for fixed-rate mortgages, including refinancing when market rates fall by a threshold or…
The document considers how to speed up repricing American equity options after constructing implied volatility surfaces. It describes the existing workflow of smoothing end-of-day surfaces and applying finite-difference pricing with discrete dividends, then…
The document discusses how to choose regression basis functions in the Longstaff–Schwartz least squares Monte Carlo method for valuing American-style options, including real options with multiple risk factors. The question is whether the few Laguerre…
The document asks how to define option vega when volatility varies with the underlying asset price, using the CEV form in which local volatility is proportional to a power of the asset price. It contrasts this setting with Black–Scholes, where volatility is…
The document questions the assumption behind conventional strategy optimization: that the process generating historical market data remains stable. It notes that out-of-sample checks and periodic reruns can help address overfitting, but may not resolve the…
A unilateral extinguisher is a swap portfolio that may be canceled after a credit event affecting one counterparty. Whether it ends depends on whether its mark-to-market value is above a contractually set threshold; a recovery payment may also apply. This…
The document introduces a two-good exchange economy with two individuals and asks how a Walrasian auctioneer's price adjustments relate to equilibrium stability. The proposed tâtonnement rule raises a good's price when it has excess demand and lowers it when…
The note considers an Itô integral of a deterministic function against Brownian motion and explains why it has zero mean, a covariance determined by the overlap of the integration intervals, and Gaussian distributions. The mean follows from the martingale…
The note works through a 97.5% expected shortfall calculation for two independent bond portfolios. Each portfolio has two possible loss amounts, and independence lets the combined outcomes be enumerated: both portfolios incur the smaller loss, one incurs…
The note explains how to reverse the order of integration in a time integral of Brownian motion, expressing the result as a stochastic integral with the differentials in the opposite order. The original integration region has time variable s between zero and…
The document considers a perpetual monthly payment obligation issued in exchange for an initial cash amount, with the issuer able to terminate it after a waiting period by repaying that original amount. It identifies the arrangement with a perpetual bond or…
The document derives a Black–Scholes–Merton value for a call-like payoff that is positive when the terminal asset price exceeds the strike and scales with the reciprocal of that price. It rewrites the payoff using an indicator and inverse asset, relating the…
The document explains why greater market volume generally lowers trading costs and how to measure execution cost. It proposes comparing the trade’s volume-weighted average price with the mid price when the order was sent, adjusting for whether the trade was…
The document examines whether arbitrage-free pricing forces zero-coupon bond prices or spot rates to move monotonically with maturity. The question derives a presumed declining spot-rate curve from an assumed monotonic increase in bond prices, then notes…
The document explains why the choice of discount rates changes a bond duration measure. Traditional Macaulay duration discounts each cash flow using the bond’s single yield to maturity, then weights its payment time by the present value of that cash flow…
The document asks how to assess whether a GARCH(1,1) volatility forecast is significantly above realized volatility. It describes a proposed approach: apply an F-test to the ratio of forecasted and realized volatility, then determine the degrees of freedom…