A non-dividend-paying stock has a current price of S0 = 400p. Over each of the next three years its price could increase by 20% (so St+1 = 1.2St), or decrease by 20% (so St+1 = St/1.2). The continuously compounded risk-free rate is 6% p.a. The stock price move in each year is independent of the move in other years.

A non-standard derivative pays off S3 after 3 years, provided that at some point over three years the stock price has moved up in one year and then immediately down in the following year. Otherwise, the derivative pays zero.

Calculate the current price of this non-standard derivative.