Pricing a call on a 130-or-70 one-year tree

A stock is at $100 and in one year will be either $130 or $70, with real-world probabilities $0.8$ and $0.2$. Interest rates are zero. What is a one-year European call with strike $110 worth?

$10. The risk-neutral up probability solves $130q + 70(1-q) = 100$, so $q = 0.5$. The call pays $20$ in the up state, so it is worth $0.5 \times 20 = 10$. The real-world $0.8$ and $0.2$ do not enter the price; replicating with $1/3$ share and borrowing $70/3$ gives the same $10$.