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3693Density Tilt Removing Carry from a Basis ProcessUnder P, a factor satisfies dX t = 0.9 dt + 0.3 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0?随机过程中等derivation未尝试面试订阅3694Density Tilt Lifting a Negative Drift Above ZeroUnder P, a factor satisfies dX t = -0.2 dt + 0.4 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0.1?随机过程中等derivation未尝试面试订阅3696Second Factor Drift After Neutralizing the First CarryUnder P, two processes share the same Brownian driver: dX t = 1.2dt + 0.6dW t and dY t = 0.5dt + 0.25dW t. If Q is chosen so that X has drift 0.3 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3697Co-Moving Spread Drift After Re-Centering the BenchmarkUnder P, two processes share the same Brownian driver: dX t = 0.7dt + 0.4dW t and dY t = -0.2dt + 0.9dW t. If Q is chosen so that X has drift -0.1 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3698Macro Factor Drift After Removing a Reference PremiumUnder P, two processes share the same Brownian driver: dX t = 0.5dt + 0.25dW t and dY t = 0.15dt + 0.35dW t. If Q is chosen so that X has drift 0 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3700Auxiliary Process Drift After Calibrating a Target ProcessUnder P, two processes share the same Brownian driver: dX t = 0.3dt + 0.2dW t and dY t = 0.45dt + 0.1dW t. If Q is chosen so that X has drift -0.05 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3701Linear Desk PnL Drift Target from a Shared DriverUnder P, dX t = 0.8dt + 0.4dW t and dY t = 0.3dt + 0.2dW t share the same Brownian motion. Let L t = 2X t + 1Y t. If Q is chosen so that L has drift 0.6 under Q, what theta is required and what is the resulting Q-drift of X?随机过程中等derivation未尝试面试订阅3702Spread Drift Target via One Girsanov TiltUnder P, dX t = 0.7dt + 0.5dW t and dY t = 0.2dt + 0.4dW t share the same Brownian motion. Let L t = 1X t + -1Y t. If Q is chosen so that L has drift -0.1 under Q, what theta is required and what is the resulting Q-drift of X?随机过程中等derivation未尝试面试订阅3706Other Factor Drift After Making a Stock Discounted Price DriftlessA traded underlier satisfies dS t/S t = 0.09dt + 0.25dW t under P, while another factor satisfies dY t = 0.2dt + 0.4dW t with the same Brownian driver. If Q is chosen so the discounted stock has drift 0 at rate r = 0.03, what is the drift of Y under Q?随机过程中等derivation未尝试面试订阅3707Convenience-Yield Drift Under the Pricing MeasureA traded underlier satisfies dS t/S t = 0.12dt + 0.3dW t under P, while another factor satisfies dY t = -0.1dt + 0.15dW t with the same Brownian driver. If Q is chosen so the discounted stock has drift 0 at rate r = 0.04, what is the drift of Y under Q?随机过程中等derivation未尝试面试订阅3711Why Girsanov Changes Drift but Not Instantaneous VolatilityUnder a standard Girsanov tilt, why do drift coefficients change while instantaneous diffusion loadings stay the same?随机过程中等essay未尝试面试订阅3712Same Paths, Different Weights Under P and QWhat does it mean to say that P and Q describe the same path space but assign different likelihood weights to paths?随机过程中等essay未尝试面试订阅3713Why Integrability Conditions Matter in GirsanovWhy do conditions such as Novikov's criterion matter when applying Girsanov in practice?随机过程中等essay未尝试面试订阅3714Why a Single Tilt Moves All Co-Driven Factors TogetherIf two factors share the same Brownian driver, why does calibrating the Girsanov tilt from one factor automatically change the other's drift as well?随机过程中等essay未尝试面试订阅3715Why Girsanov Is Useful for Pricing Even When Physical Drift Is InterestingWhy is Girsanov still useful in pricing problems even when a researcher cares about the physical drift of the process?随机过程中等essay未尝试面试订阅3716Forecasting Client Inventory PnL Versus Marking an Embedded OptionA desk wants a distribution for next month's realized client-inventory PnL, but it also needs today's fair value for an embedded option inside that inventory. Which measure belongs to each task, and why are the answers not contradictory?随机过程中等essay未尝试面试订阅3717Historical Carry Is High but the Pricing Drift Is LowA junior notices that a commodity future has shown high historical carry under the data, yet the desk prices an option on that future under a measure with much lower effective drift. How should you explain the gap?随机过程中等essay未尝试面试订阅3718Backtesting a Signal Versus Pricing Its Optional OverlayA PM is backtesting a signal-driven strategy and also wants to value a stop-loss overlay that behaves like an option. Which measure should dominate each part of the workflow?随机过程中等essay未尝试面试订阅3719Stress Testing a Hedge Book Versus Marking It TodayRisk asks for a stress distribution of tomorrow's hedge-book PnL, while front office asks for today's mark of the same book. Should both use the same measure?随机过程中等essay未尝试面试订阅3720Why VaR and Option Price Should Not Share a Drift Assumption by DefaultWhy is it usually a mistake to force the same drift assumption into both VaR simulations and derivative pricing models?随机过程中等essay未尝试面试订阅