Final answer:
The simulated value of the stock price for tomorrow using generalized Brownian Motion, with given parameters, is approximately $139.28, which is closest to the option (a) $139.32.
Step-by-step explanation:
To simulate the stock price for tomorrow using generalized Brownian Motion, we use the formula for Geometric Brownian Motion (GBM):
S(t) = S(0) * exp((μ - σ²/2) * t + σ * Z * sqrt(t))
Where:
- S(0) = current stock price = $135
- μ = daily growth rate = 0.03
- σ = daily volatility = 0.04
- t = time period = 1 day
- Z = random sample from a normal distribution = 0.031466
Plugging in the values, we get:
S(1) = $135 * exp((0.03 - 0.04²/2) * 1 + 0.04 * 0.031466 * sqrt(1))
First, we calculate (0.03 - (0.04² / 2)):
0.03 - (0.04² / 2) = 0.03 - 0.0008 = 0.0292
Now we can substitute this value back into the equation:
S(1) = $135 * exp(0.0292 + 0.04 * 0.031466)
Expanding the exponential part:
exp(0.0292 + 0.04 * 0.031466) = exp(0.03045864)
The final calculation of tomorrow's stock price is:
S(1) = $135 * exp(0.03045864) ≈ $135 * 1.030958103 = $139.28
Therefore, the simulated value of the stock price for tomorrow is approximately $139.28, which is closest to the option (a) $139.32.