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An investor has invested $50,000 in a stock. Denote by <math>S_t</math> the stock price at time <math>t</math> expressed in years with <math>S_0</math> the current stock price. Suppose <math>\ln(S_t/S_0) </math> is normally distributed with mean <math>\mu = 0.05t </math> and standard deviation <math>\sigma = 0.1\sqrt{t} </math>. Determine the 99<sup>th</sup> percentile for the investor's $50,000 investment for a 30 day period. | An investor has invested $50,000 in a stock. Denote by <math>S_t</math> the stock price at time <math>t</math> expressed in years with <math>S_0</math> the current stock price. Suppose <math>\ln(S_t/S_0) </math> is normally distributed with mean <math>\mu = 0.05t </math> and standard deviation <math>\sigma = 0.1\sqrt{t} </math>. Determine the 99<sup>th</sup> percentile for the investor's $50,000 investment for a 30 day period. | ||
< | <ul class="mw-excansopts"> | ||
<li>[46000, 50000]</li> | <li>[46000, 50000]</li> | ||
<li>[52000, 55000]</li> | <li>[52000, 55000]</li> | ||
| Line 7: | Line 7: | ||
<li>[75000, 77000]</li> | <li>[75000, 77000]</li> | ||
<li>[77000, <math>\infty</math>]</li> | <li>[77000, <math>\infty</math>]</li> | ||
</ | </ul> | ||
Revision as of 13:07, 18 March 2024
An investor has invested $50,000 in a stock. Denote by [math]S_t[/math] the stock price at time [math]t[/math] expressed in years with [math]S_0[/math] the current stock price. Suppose [math]\ln(S_t/S_0) [/math] is normally distributed with mean [math]\mu = 0.05t [/math] and standard deviation [math]\sigma = 0.1\sqrt{t} [/math]. Determine the 99th percentile for the investor's $50,000 investment for a 30 day period.
- [46000, 50000]
- [52000, 55000]
- [58000, 60000]
- [75000, 77000]
- [77000, [math]\infty[/math]]