Assume that the ABC stock pays no dividend and is currently priced at $S0 = \$10$.
Assume that, at the expiry time $T > 0$, the stock price goes up to $u*S0$ with probability $0 < p < 1$ and down to $d*S0$ with probability $1 − p$. We know that $d < 1 < u$ but do not know $d$ or $u$.
Assume that there is no arbitrage and the interest rate is zero.
Consider the following three options with the same expiry $T$ on the ABC stock. Assume that a European put option with strike price $\$9$ is priced at $\$ 14/9$ while a European put option with strike price $\$8$ is priced $\$ 8/9$.
What is the fair value of a European call option with a strike price of $\$7$? Explain your answer.
I'm having trouble solving this question. I have never dealt with such questions before and have no background in finance. I'd appreciate any help any one can give, thanks!