Question

A stock with a current price of $25 will either move up to $32 or down to $20 over the next period. the risk-free rate of interest is 3.5%. what is the value of a call option with a strike price of $30?

O $.68
O $.74
O $.95
O $1.12
O $1.31

Answer 1

To calculate the value of a call option with a strike price of $30, we need to consider the potential outcomes and probabilities. The value of a call option with a strike price of $30 is approximately $26.13.

Step-by-step explanation:

To calculate the value of a call option with a strike price of $30, we need to consider the potential outcomes and probabilities. In this case, the stock price can either increase to $32 or decrease to $20. The risk-free rate of interest is 3.5%. Using the formula for the value of a European call option, we can calculate:

Value of call option = (probability of increase * present value of potential increase) - (probability of decrease * present value of potential decrease)

Let's calculate:

Probability of increase = (32 - 25) / (32 - 20) = 7 / 12

Probability of decrease = 1 - Probability of increase = 5 / 12

Present value of potential increase = 32 / (1 + 0.035) = 30.86

Present value of potential decrease = 20 / (1 + 0.035) = 19.40

Value of call option = (7/12 * 30.86) - (5/12 * 19.40) = 42.30 - 16.17 = 26.13

Therefore, the value of a call option with a strike price of $30 is approximately $26.13.