Let V (t, St ) be the value of this portfolio. That is: V(t, St ) = -f(t, St )+ df/ds*St so The pure investment gain over the period (t, t +dt] is the change in the value of the minus one derivative plus the change in the value of the holding of df/ds units of the share. That is: dV(t, St ) = -df(t,St )+ df/ds*dSt then, -df(t,St )+ df/ds*dSt=(-df/dt-1/2*d2f/ds2*var*St2)*dt Note that this portfolio strategy is not self-financing. That is, the pure investment gain derived above is not equal to the instantaneous change in the value of the portfolio, dV (t St ) . where , dSt =St(udt+o*dZt) where St is the share price & f(t, St) is the derivative value can anyone please explain me the underlined part ?thanks in advance
Self-financing is defined formally in Chapter 15, Section 1.3. So, this may seem better once you've read further in the notes. The following thread should help to answer your query: https://www.acted.co.uk/forums/inde...e-in-the-risk-free-portfolio.4608/#post-17972 Note that this comment on self-financing is just an aside in the derivation of the Black-Scholes PDE. If you follow the rest of what appears, don’t let this throw you off course.
