Financial Risk Manager Part 1
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A trader seeks to calculate the price of a European-style call option with a strike price of USD 30.00 and a 6-month expiration. It is observed that a 6-month European-style put option on the identical stock with the same strike price of USD 30.00 is priced at USD 4.00. The current stock price is USD 32.00, and the stock will pay a one-time dividend of USD 0.75 per share in 3 months. Additionally, the annual continuously compounded risk-free rate stands at 3.5%. What is the closest value to the no-arbitrage price of the call option?
A trader seeks to calculate the price of a European-style call option with a strike price of USD 30.00 and a 6-month expiration. It is observed that a 6-month European-style put option on the identical stock with the same strike price of USD 30.00 is priced at USD 4.00. The current stock price is USD 32.00, and the stock will pay a one-time dividend of USD 0.75 per share in 3 months. Additionally, the annual continuously compounded risk-free rate stands at 3.5%. What is the closest value to the no-arbitrage price of the call option?
Explanation:
C is correct. From the equation for put-call parity, this can be solved by the following equation: C = So + p - PV(K) - PV(D) where PV represents the present value, so that: PV (K) = K * e^(-rT) and PV (D) = D * e^(-rt) where: p is the put price = USD 4.00 c is the call price = to be determined K is the strike price of the put option = USD 30.00 D is the dividend = USD 0.75 So is the current stock price =USD 32.00 t is the time to the one-time dividend = 3/12 = 0.25 T is the time to expiration of the option = 6/12 = 0.5 r is the annual risk-free rate of interest = 3.5% Calculating Pv(K), the present value of the strike price results in a value of 30.00 * e^(-00350.5) or 29.4796, while PV(D) is equal to 0.75 * e^(-0035*0.25) = 0.7435. Hence, C = 32.00 + 4.00 - 29.4796 - 0.7435 = USD 5.7769.