Van, Inc. stock is selling for $38 a share. The 6-month 35 call on Van, Inc. stock is selling for $5.97 while the 6-month 35 put is priced at $1.85. What is the continuously compounded risk-free rate of
Return?

Question

Quizplus · Accepted Answer

Using the put-call parity formula:

Call price - Put price = Stock price - Present value of the strike price 
$5.97 - $1.85 = $38 - PV(35)

Solving for PV(35), we get:

PV(35) = $33.82

Now we can use the formula for the continuously compounded risk-free rate of return:

r = [ln(S/PV(K))+(δ + σ²/2)t]/(σ√t)

Where: 
S = stock price = $38 
PV(K) = present value of the strike price = $33.82 
δ = dividend yield (not given so assumed to be zero) 
t = time to expiration in years = 0.5 
σ = annualized standard deviation of the stock's returns (not given so assumed to be 30%)

Plugging in the numbers:

r = [ln($38/$33.82) + (0 + 0.3²/2)(0.5)]/(0.3√0.5) 
r = 0.0650 or 6.50%

Therefore, the answer is (B) 6.50 percent.

Van, Inc Stock Is Selling for $38 a Share