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Chapter 16 practice bank

100 questions:
Stochastic Calculus

Solve on paper first. Reveal only the final answer when you want to check yourself. There are no worked solutions in this bank by design.

34 easy 33 medium 33 advanced

EasyFair random walkstochastic-processes-calculus-1

After 9 independent fair ±1 steps, find the position mean and standard deviation.

EasyBrownian incrementsstochastic-processes-calculus-2

For standard Brownian motion, give the distribution of W_3−W_1.

EasyOne-step Markov transitionstochastic-processes-calculus-3

A two-state chain currently in A stays in A with probability 0.7. Give its next-state distribution (A,B).

EasyStationary distributionstochastic-processes-calculus-4

For P=[[1−0.2,0.2],[0.3,1−0.3]], find stationary π.

EasyMartingale definitionstochastic-processes-calculus-5

Mₙ is a martingale and Mₙ=5. What is E[Mₙ₊₁ | 𝔽ₙ]?

EasyEuler-Maruyamastochastic-processes-calculus-6

For dX=2dt+1dW, start X=4, use Δt=0.04 and Z=0.5. Find one Euler step.

EasyGBM solutionstochastic-processes-calculus-7

For GBM S₀=100, μ=0.04, σ=0.2, t=1, W₁=0, find S₁.

EasyBrownian covariancestochastic-processes-calculus-8

Find Cov(W_2,W_7) for standard Brownian motion.

EasyFair random walkstochastic-processes-calculus-9

After 16 independent fair ±1 steps, find the position mean and standard deviation.

EasyBrownian incrementsstochastic-processes-calculus-10

For standard Brownian motion, give the distribution of W_5−W_2.