Stochastic Calculus

Practice problems for Stochastic Calculus

• Brownian Motion: Compute E[W_s W_t]
• Ito Isometry: Var(∫ W_t dW_t)
• Martingale Property: E[W_t | F_s]
• Quadratic Variation of Brownian Motion
• Ito’s Lemma: Drift of log(S_t) under GBM
• Risk-Neutral Drift with Continuous Dividend Yield
• Explicit Solution to GBM
• Feynman–Kac: PDE to Expectation
• Girsanov: Brownian Motion under Measure Change
• Ornstein–Uhlenbeck Process: Mean Function