Let and be two positive constants such that .

Suppose denotes the price of a risky asset at time and consider a filtered probability space such that for every .

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 and (respectively) and strike prices and (respectively).

Question.

Suppose the (effective) rate of interest is constant and equal to 2% (per time step), the initial stock price is = $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.