Suppose that the price of a stock follows the equation from Black-Scholes-Merton:

S_t = S_(t-1) + S_(t-1)T + S_(t-1)sqrtTe

Where S_t is the current price, S_(t-1) is the previous price one period back, is the expected return on the stock determined by CAPM, T is the time between the current price and the previous price as a fraction of a year, is the volatility of the price, and e is a random error term.

What are delta, gamma, theta, vega, and rho for this stock? (if you feel you cannot come up with a specific number for any of these five measures, then just describe what they are likely to be in words i.e. positiveegative, large/small, etc.)

[These measures would be defined very generally here as sensitivity to the risk factor. For example, delta is sensitivity to changes in the price of the stock, theta is sensitivity to the passing of time, etc.]

Please show reasoning with explanations.

= S(t-1)+ Sct-buT + S(t-10VTe = S(t-1)+ Sct-buT + S(t-10VTe