Using the following example can someone explain to me why the put is more expensive in part a and why the call is more expensive in part b?
$$C_E-P_E=S(0)-X \cdot \frac{1}{1+R}$$ where $X$ is the strike price.
Assume that the stock price is governed by a binomial model. The initial price of the stock is $S(0)=100$. The return on a risk-less security over one period of time is $R=10\%$. The parameters $u$ and $d$ are not known.
a. Which of the following two options is more expensive: A European put option with strike $120$ and expiration $1$ or a European call option with strike $120$ and expiration $1$?
b. Which of the following two options is more expensive: A European put option with strike $110$ and expiration $2$ or a European call option with strike $120$ and expiration $2$?
for part a I get $C_E-P_E=100-120 \cdot \frac{1}{1+0.1}$
and I know $100-120 \cdot \frac{1}{1+0.1} \lt 0$
but why does this mean the put is more expensive?