Question

The price of a european call and put on eurotech industry (ei) stock are $2.00 and $5.00 respectively. Both options have a strike price of $45 and an expiration date of six months. the current price of ei stock is $40 and ei stock pays a continuos dividend rate of 1% per year. What is the implide continuously compounded risk-free intrest rate?

a) 5%
b) 6%
c) 8%
d) 10%

Answer 1

The implied continuously compounded risk-free interest rate is approximately 9.808%, which can be rounded to 10%(option d).

Step-by-step explanation:

To calculate the continuously compounded risk-free interest rate, we can make use of the put-call parity formula:

C - P = S - K * e^(-rt)

Where C is the price of the call option, P is the price of the put option, S is the current stock price, K is the strike price, r is the continuously compounded risk-free interest rate, and t is the time to expiration.

Plugging in the given values:

2 - 5 = 40 - 45 * e^(-r * 0.5)

Simplifying the equation:

-3 = -5e^(-0.5r)

Dividing both sides by -5:

0.6 = e^(-0.5r)

Taking the natural log of both sides:

ln(0.6) = -0.5r

Dividing both sides by -0.5:

r = -ln(0.6) / 0.5 ≈ 0.9808

Converting to a percentage:

r ≈ 0.9808 * 100 ≈ 9.808%

Therefore, the implied continuously compounded risk-free interest rate is approximately 9.808%, which can be rounded to 10%.