So I'm enrolled in a Mathematics for Finance course, and we received this question on the last Problem Set. I'm completely stuck on how to solve this problem. I tried applying the formula xS(t) + yA(t) = C(t), but I get stuck with figuring out A(t) - which represents the price of bonds.
Any help on this would be appreciated. I'm baffled on how to continue with this.
Hints: In a one-period market the discount factor is $1/(1+i)$ where $i$ is the risk-free interest rate. The price of the put option is the discounted expected value of the payoff, $\max(0,K-S(T))$, where the expectation is taken with respect to risk-neutral probabilities $q_u$ and $q_d$. In the risk-neutral world the expected future stock price is the forward price $S_0(1+i)$. Solve for the risk-neutral probabilities by equating the forward price with this expectation. Then go back and price the option.