Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 29K / b / Solution

{c}

For a discounted claim $H$, the arbitrage-free value process is $V_t=\mathbb E_Q[H\mid\mathcal F_t]$. A terminal payoff $h(S_T)$ has value
$$
V_t=\sum_{k=0}^{T-t}\binom{T-t}{k}q^k(1-q)^{T-t-k}
h(S_tu^kd^{T-t-k}).
$$


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 Incoming links: Risk-neutral valuation in the Cox--Ross--Rubinstein model