Question

A call option has an exercise price of $70 and matures in six months. The current stock price is $71, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of the call if the standard deviation of the stock is 0 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Call option price

$

Answer 1

Answer,

The theoretical minimum value of call option=spot price(S)-Present value of strike price(X)

Information given,

S=71

X=70

t=6/12(6 months)

rf=4% or 0.04 (risk-free rate)

STEP 1 Present value of the strike price

PV of strike price=Strike price * e^-rft

e^-rft=e^-0.04*6/12

e^-0.02=1.0202

e^-0.02=1/1.0202=0.9802

PV of strike price=70*0.9802=68.614

The theoretical minimum value of call option

The theoretical minimum value of call option=spot price(S)-Present value of strike price(X)

=71-68.614=2.39

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