Other questions based on the Formula Sheet (Pt. 2)

Question 1

What is the formula for the delta-gamma-theta approximation?

Answer 1

V(t+h) = V(t) + Delta(t)(epsilon) + 0,5Gamma(t)(epsilon^2) + Theta(t)h
where epsilon = S(t+h) - S(t)

Question 2

What is the formula for the market-maker’s profit on a delta-hedged portfolio?

Answer 2

-0,5Gamma(t)(epsilon^2) - Theta(t)h - ((e^rh) - 1)(Delta*S(t)-V(t))
where
epsilon = S(t+h) - S(t)
((e^rh) - 1) = rh if h is small