Assume that the asset price follows geometric Brownian motion where X and Y are two no-arbitrage…

Assume that the asset price follows geometric Brownian
motion  

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where X and Y are two no-arbitrage assets. Show that a
portfolio Pt which is given by

is self-financing. Show that the portfolio Pt is
self-financing when

 

and prove this relationship using the Ito’s formula.

Assume a geometric Brownian motion model for XY (t).
Determine which of the following portfolios are self-financing:

Show that the difference between the futures price and
the forward price satisfy

 

Chapter 2