Why are you being assigned homework involving algebra and calculus when you haven't yet taken those courses? :shock:
Never had those courses and never had math at this level haha so everything went well until...
So V is a function of S? And the derivative will be V'(S) = dV/dS?
The whole idea is as follows. Assuming a stock follows an ito process. Then, a derivative (for instance a call option or put option or any other contract that derives its value from the stock) can be calculated by using the ito lemma.
Based on that, I think the v is a function of S. The only thing i know is that I have to take the first derivative and second derivative of the formula:
V = S(1/1)e0.4(1-t)
and the first derivative with respect to time. However, T is not given. So im still in doubt whether or not to use a 0 for t or just t in there. But leaving t in these makes is quite hard to find the derivatives.
What do you mean by "filling in an equation"? How does "v" relate to "V", if at all? With respect to what variable is the derivative taken (that is, what is underneath the "dv")?
(VS(α−d)S+Vt+12V″(σS)2)Dt+V′σSd
I have to fill in the above equation. VS is the first derivative of the formula
V = S(1/1)e0.4(1-t)
α = 0.14, d = 0.01, 2V is the second derivative. VT, is the first derivative with respect to time.
If t = 0 then the first derivative is e
0.4s, the second is 0 and the derivative with respect to time is 0 as well. However, I think that T is not zero per definition. The formula just indicates that there is a time component
So my first questions here are whether or not to take derivative with t being t. And what the derivatives (first, second and time) are? If I know these values, then VS can be replaced by the first derivative, (0.14-0.01)S, VT derivative of time component and 2V'' the second derivative. Sigma is 0.48.
Are these maybe the "instructions"...? (If "substitute S in formula dv with the inverse of e(2/5)" indicates "the question", then I'm not understanding the question.)
Okay, the above formula (VS(a-d).... is now filled in with the numbers and derivatives. However, since S is in the formula it is still a function for the stock price. Thus, in order to value the derivative (call option e.g.) S has to be substituted by V.
V in this case is the inverse of
V = S(1/1)e0.4(1-t) .
L
acking a context (additive inverse, multiplicative inverse, functional inverse if we're saying "y = e^x; find inverse statement, given x = 2/5", etc), I'm not sure.
No idea. See above.
What is the "ito process"? Does "Vs" mean "the first derivative of V with respect to s, or with respect to S, or with respect [see below] to \(\displaystyle \delta\))? (Similar question for "Vss".)
Vs means the first derivative of the formula
S(1/1)e0.4(1-t) . This applies to Vss (second derivative) and Vt (derivative of time) as well
As originally posted, there was no \(\displaystyle \alpha,\, \delta,\,\) or \(\displaystyle \sigma.\) How do these relate?
Also, does the above mean that the "ito lemma" is as follows?
(VS(α−d)S+Vt+12V″(σS)2)Dt+V′σSd
yes, see above. This is the formula that has to filled in.
Which derivative is this? What do you mean by "the value" of the derivative, when the right-hand side does not actually simplify to a numerical value? What do you mean by "can be described by"?
You have to take the derivatives of equation
S(1/1)e0.4(1-t) fill it into the equation (ito lemma) and substitute S by the inverse of
S(1/1)e0.4(1-t) . in order to value a derivative (a call option or contract that depends on the value of a stock)
How did you arrive at this?
Taking the derivatives of the formula
V = S(1/1)e0.4(1-t) and fill it into the equation. However, It think my derivatives of the equation are wrong.
Which formula? How?
Please reply
showing all of your work. Thank you!