Evaluating contract $D$ where the stock follows the Black Scholes assumption

Ch.7 Mark Joshi Problem 14

A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-Scholes formula for the price of $D$.

Attempted solution - Seems to me that we have $$0.3\times(S_1 - S_0)_{+}$$ so we are evaluating a call option struck at $S_0$ and we need to multiply by $0.3$ to get the price. Although, the solution by Mark Joshi does the same but divides $0.3$ by $S_0$, no idea why and where that came from.

• The difference is just that you understood "increase" to mean absolute increase, i.e. $S_1 - S_0$, while it seems like Joshi meant the percentage increase/return $\left( S_1 - S_0 \right) / S_0$. Given the question, I would have interpreted it the same way as you did. – LocalVolatility Feb 1 '18 at 23:17