A non-dividend paying stock's price follows the Ito process:
dS(t) / S(t) = .12dt +.3dZ(t)
Another non-dividend paying stock has a price which follows the Ito process:
dQ(t)/Q(t) = .3dt +.9 dZ(t)
S(0)=40
Q(0)=5
A risk-free portfolio requiring no cash outlay consists of 100 shares of S and x shares of Q, and a bond of value K earning the risk-free rate.
Determine x.
Answer: This time we'll arrange for the dZ(t) coefficients to add up to 0. Since we want to cancel out dZ(t), we need to sell an amount of Q having 1/3 the value of the amount of S that we own. Since we own 100(40)=4,000 of S, we need to sell Q having a value of 4000/3, which means
x=-800/3.
Can someone please explain to me the formulas used to solve this? I am not understanding how x was found.
dS(t) / S(t) = .12dt +.3dZ(t)
Another non-dividend paying stock has a price which follows the Ito process:
dQ(t)/Q(t) = .3dt +.9 dZ(t)
S(0)=40
Q(0)=5
A risk-free portfolio requiring no cash outlay consists of 100 shares of S and x shares of Q, and a bond of value K earning the risk-free rate.
Determine x.
Answer: This time we'll arrange for the dZ(t) coefficients to add up to 0. Since we want to cancel out dZ(t), we need to sell an amount of Q having 1/3 the value of the amount of S that we own. Since we own 100(40)=4,000 of S, we need to sell Q having a value of 4000/3, which means
x=-800/3.
Can someone please explain to me the formulas used to solve this? I am not understanding how x was found.
Example 20F ASM Manual - Risk Free Portfolios
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