In: Finance

# Why should the option premium decrease with the strike price?

Suppose the stock price is $40 and the effective annual interest rate is 8%. a. Draw on a single graph payoff and profit diagrams for the following options: (i) 35-strike call with a premium of$9.12.

(ii) 40-strike call with a premium of $6.22. (iii) 45-strike call with a premium of$4.08.

b. Consider your payoff diagram with all three options graphed together. Intuitively, why should the option premium decrease with the strike price?

## Solutions

##### Expert Solution

Given that the EAR = 8%

• 35-strike call with a premium of 9.12 • \begin{align*} \text{purchased call payoff} &= \max(0, \text{spot price at expiration} - \text{strike price})\\ &= \max(0, S - 35)\\ &= \begin{cases} 0 & S<35 \\ S-35 & S\geq 35 \end{cases} \\ \text{purchased call profit} &= \max(0, \text{spot price at expiration} - \text{strike price}) - \text{future value of option premium} \\ &= \max(0, S-35) - 9.12(1.08) \\ &= \max(-9.8496, S-35-9.8496)\\ &= \max(-9.8496, S-44.8496)\\ &= \begin{cases} -9.8496 & S<35 \\ S-44.8496 & S\geq 35 \end{cases} \end{align*} • 40-strike call with a premium of6.22
• \begin{align*} \text{purchased call payoff} &= \max(0, \text{spot price at expiration} - \text{strike price})\\ &= \max(0, S - 40)\\ &= \begin{cases} 0 & S<40 \\ S-40 & S\geq 40 \end{cases} \\ \text{purchased call profit} &= \max(0, \text{spot price at expiration} - \text{strike price}) - \text{future value of option premium} \\ &= \max(0, S-40) - 6.22(1.08) \\ &= \max(-6.7176, S-40-6.7176)\\ &= \max(-6.7176, S-46.7176)\\ &= \begin{cases} -6.7176 & S<40 \\ S-46.7176 & S\geq 40 \end{cases} \end{align*}
##### Price of T-Bill
What is the price of a T-Bill 98 days prior to maturity if the face amount is 100 and the yield (the simple interest rate) is 2.7% per annum.