Tag Info

Hot answers tagged

7

You should look at Paul Willmott's Frequently Asked Questions In Quantitative Finance. He offers 12 (I think) ways of deriving BS and I think you'll find what you look for there. The cool thing is that you really have many different approaches; one is the classic PDE, one is done using change of measure, one is done using binary trees, and so on.... Really ...


5

Specifically, we have a generic conditional claim, $C$, that is a function of the diffusion process for the underlying, $S(t)$, and time $t$ so $C = C(S(t), t)$. As you pointed out, $C$ is an Ito process becuase it is a function of a stochastic process so we use Ito's Lemma to determine how the contingent claim varies as a function of the diffusion process ...


2

I agree with vanguard2k's comment: A few more details on the notation would be helpful. But, as far as I can tell, the second equality is a simple expansion. First, $\mathbf{1}'\mathbf{1} = T$ (assuming the vectors are elements of $\mathbb{R}^T$). The expression $\mathbf{1} (\mathbf{1}'\mathbf{1})^{-1} \mathbf{1}'$ is therefore nothing else than a $T\times ...


1

What is the data basis that you start from? If you just have the covariance matrix, then you can only calculate portfolio variance or volatility by $$ w^T \Sigma w$$ where $w$ are the portfolio weights and $\Sigma$ is the covariance matrix. If you have the individual asset continuously compounded returns $r^j_t$ where $j$ indexes assets, $j=1,\ldots,N$, and ...



Only top voted, non community-wiki answers of a minimum length are eligible