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Changing the measure · Part 4 of 4

Under the real-world measure PP a stock follows dSt=μSt dt+σSt dWtdS_t = \mu S_t\,dt + \sigma S_t\,dW_t with μ=10%\mu = 10\% and σ=20%\sigma = 20\%. The risk-free rate is r=2%r = 2\%.

What is the density dQdP∣FT\left.\frac{dQ}{dP}\right|_{\mathcal{F}_T} that makes WQW^Q a Q-Brownian motion?

  1. Aexp⁡(+θWT−12θ2T)\exp\left(+\theta W_T - \tfrac{1}{2}\theta^2 T\right)
  2. Bexp⁡(−θWT−12θ2T)\exp\left(-\theta W_T - \tfrac{1}{2}\theta^2 T\right)
  3. Cexp⁡(−θWT+12θ2T)\exp\left(-\theta W_T + \tfrac{1}{2}\theta^2 T\right)
  4. Dexp⁡(−θWT)\exp(-\theta W_T)

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Changing the measure, part 4 of 4 · QuantMax