Let $\displaystyle T_1$ and $\displaystyle T_2$ be two positive constants such that $\displaystyle T_2 > T_1$.

Suppose $\displaystyle S_t$ denotes the price of a risky asset at time $\displaystyle t$ and consider a filtered probability space $\displaystyle (\Omega, F, \{F_t\}_{0 \leq t \leq T_2} , \mathbb{P})$ such that $\displaystyle F_t := \sigma(S_u : 0 \leq u \leq T_2)$ for every $\displaystyle t \in [0, T_2]$.

Then, one may consider a (European-type) option written on another (European-type) option, i.e. a compound option.

A typical example of a compound option is `a put on a call', where both put and call are European-type options with maturity dates $\displaystyle T_1$ and $\displaystyle T_2$ (respectively) and strike prices $\displaystyle K_1$ and $\displaystyle K_2$ (respectively).

Question.

Suppose the (effective) rate of interest is constant and equal to 2% (per time step), the initial stock price is $\displaystyle S_0$ = $50 and it can rise by 5% or fall by 2% at time 1, and again also at time 2.

Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call').

The italic bit is the bit I can't understand,it doesn't seem to make any grammatical sense. Someone fancy translating it? This was an exam question as well, I would've surely kicked up fuss about it afterwards.