A non$-$dividend paying stock has a current price of R$100.$ In any unit of time the price of the

stock is expected to increase by $10\%$ or decrease by $5\%.$ The continuously compounded risk$-$free

interest rate is $4\%$ per unit of time.

A European call option is written with a strike price of R$103$ and is exercisable after two units of

time, at t $=2.$

Establish, using a binomial tree, the replicating portfolio for the option at the start and end of

the first unit of time, i$.$e$.$ at t $=0,1.$ Hence, calculate the value of the option at t $=0.[20]$