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The document tests whether the process formed by multiplying one standard normal random variable by the square root of time is Brownian motion. Although each value has a normal distribution with mean zero and variance equal to time, those marginal…
The document describes a time-series analysis of European equity industry portfolio returns against Fama–French factor returns, with momentum included in one model. The portfolios include a value-weighted portfolio and equally weighted portfolios formed by…
The document explains how Greeks for swaptions, caps, floors, and other interest rate options are defined and calculated. They measure sensitivity of a derivative’s value to pricing inputs. Because interest rate pricing depends on an entire curve, the…
The document explains the drift in the extended Vasicek, or Hull–White, short-rate model. Under the risk-neutral measure, the short rate follows a mean-reverting process with a time-dependent drift term and volatility. The drift is not itself the riskless…
The document considers how to choose portfolio weights that are proportional to risk budgets divided by asset volatilities, while meeting a target portfolio volatility and other constraints. It contrasts this objective with a risk-budgeting formulation that…
The document asks how to identify the most likely value associated with a call option when the underlying price is lognormally distributed. It starts from the discounted expected call payoff and distinguishes the mode of the underlying price distribution…
The document compares simulating three assets independently with simulating them jointly through a multidimensional geometric Brownian motion. In the joint approach, correlated log returns are represented using a covariance structure and Cholesky…
The document asks how to formulate a Kalman filter for return-based style analysis, where a fund’s returns are related to factor returns and the factor exposures may change over time. It proposes modeling the beta coefficients as the hidden state, perhaps…
The document examines whether adding a swap payment period changes the value of American and Bermudan swaptions in a predictable order. It defines co-terminal and co-initial swap structures, their exercise schedules, and the proposed comparisons between…
The document asks why a bank may incur a cost when it holds a positive derivative value as a receivable before cash settlement. It distinguishes the economic profit implied by a future payment from cash already available to the bank, and considers whether…
The document explains why pension funds and endowments may invest directly alongside private equity or venture capital funds. Co-investment can let an institution increase its exposure to a deal it finds especially attractive beyond its proportional…
The document addresses two points about an example of VaR manipulation: a likely sign error in an inequality and how a put strategy changes reported risk and profit. The answer says the displayed ordering is consistent if the intended condition is that both…
The document asks how to price a zero-coupon bond from a short-rate model, starting with the risk-neutral conditional expectation of the exponential of the negative accumulated short rate. It names several model families and asks how simulated rates,…
The document considers why trading firms might locate near Bloomberg’s data center and relay information to New Jersey over microwave links. It distinguishes market news from information available through Bloomberg’s electronic trading platform, EMSX. The…
The document explains how floating-rate notes linked to overnight benchmarks accrue interest over a coupon period. It frames the calculations as adaptations of overnight indexed swap compounding and distinguishes simple averaging from compounding. It also…
The answer recommends separating operational monitoring from strategy monitoring when running automated trading systems. Operational checks include server heartbeats and alerts, centralized log persistence, and visibility into CPU and memory use. It…
The discussion considers whether short-term directional strategies may work better in markets with more uninformed traders. The response says uninformed flow can be valuable because it is less informed about near-term prices, but does not develop a strategy…
The document discusses which market instruments can provide data for constructing yield curves during the transition from LIBOR to SOFR. It describes the familiar LIBOR approach, which uses forward rate agreements, futures, and swaps referencing the relevant…
The document considers a bond with a call and a put exercisable on the same date, using different strikes to illustrate how the embedded options affect value. Under its stated assumptions—a forward bond price of 100 and no discounting—the example values the…
The document addresses where to obtain historical European Union Allowance futures data at intraday frequency for carbon market research. The response points to a commercial market data vendor that offers trade histories and, optionally, quote histories for…
The document explains why a historical portfolio Value at Risk calculation can return an empty result at a high confidence level. The cited implementation converts the confidence level to a lower-tail probability, multiplies that probability by the number of…
The document distinguishes reinsurance by the losses to which the retention and coverage limit apply. Stop-loss reinsurance covers aggregate losses over a period: the reinsurer pays the portion of total losses above a retention, potentially capped at a…
The document describes an attempt to infer local volatility from synthetic option prices generated under a Heston stochastic volatility model. Prices are computed with the COS method, while finite differences estimate the time derivative of call prices and…
The document asks how to derive the conditional distribution of a Brownian motion value between two observed times. Given the values at the interval endpoints, it states that the intermediate value is normally distributed, with a mean formed by linear…