Suppose the price St of an asset follows a Geometric Brownia

Suppose the price, St, of an asset follows a Geometric Brownian Motion, GBM(0, 0.5). The current price of the asset is $30. The investor plans to sell the asset when it reaches $40. How many days (on average) will he have to wait to sell?

Solution

Drift rate, = 0.5/day and Percentage Volatility rate, = 0/day

Because it is not true for geometric brownian motion with zero drift.

Present value S₀ = $30, and futute value S_t = $40.

Now our required formula is S_t = S₀*exp[(²/2)*t + *W_t]

=> 40 = 30*exp(5*t)

Since we are calculating the average time therefore_,

=> 0.5*t = ln(4/3)

=> t = 0.28768/0.5 = 0.5754 days