Stochastic Calculus Research Paper Help

Stochastic Calculus 1. Consider a basket of N assets each following the Geometric Brownian Motion, so the Stochastic Differential Equation for each asset. is given by (153? = Sillidt + SiO?idXi fOI? 1 S1 S [V The price changes are correlated as measured by the linear correlation coefficients pij. Invoke the multi-dimensional Ito Lemma to write down the SDE for F (Sl, SQ, . . . , S N) in the most compact form possible (with clear drift. and diffusion terms). Apply dXide -> pijdt. 2. Construct an SDE for the process Y(t) = e?X(t)?%?2t and show that the process is, in fact, an Exponential Martingale of the form dY(t) = Z (1?) g(t) dX (t). Identify the terms g(t) and Z (t) A diffusion process Y(t) is a martingale if its SDE has no drift term. The SDE can be constructed by evaluating partial derivatives of a function F(t, X) = Y(t) and substituting as follows: oF 1 82F 8F dF= ? ? dt -dXt. (8t+2oX2> +oX Ru Essay writing Help

Do You Need A Similar Assignment?

Place an order with us. Our skilled and experienced writers will deliver a custom paper which is not plagiarized within the deadline which you will specify.

Note; 6 Hours urgent orders deliver also available.

If you need more clarifications contact our support staff via the live chat for immediate response.

 

Type of paper Academic level Subject area
Number of pages Paper urgency Cost per page:
 Total: