értekezés - Budapesti Corvinus Egyetem

Optimal stock return volatility that maximizes the expected utility of managers’ wealth
Optimal stock return volatility
6
5
Expected utility
4
3
2
1
0
0% 10% 20% 30% 40% 50% 60%
stock return volatility
owning stock owning ITM stock option owning ATM stock option owning OTM stock option
The figure illustrates the optimal stock return volatility that is needed to maximize the
expected utility of the wealth of manager owning 1. a stock; 2. a deep in-the-money option
on the stock; 3. a near at-the-money option on the stock; or 4. a deep out-of-the-money
1 λ
option on the stock. The utility function is in the form of U = W + c . Further
λ
parameters are: S 0 = 1000; X ITM =500; X ATM =3000; X OTM = 7000; rf = 6%; q = 1%; T-t = 3
yrs; λ = -0,1; c = 10.
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