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Homework answers / question archive / Consider an option on a non-dividend-paying stock when the stock price is $30, the exe price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum the time to maturity is four months
Consider an option on a non-dividend-paying stock when the stock price is $30, the exe price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum the time to maturity is four months. a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What is the price of the option if it is a European put? d. Verify that put-call parity holds. In this case Sn = 30, K = 29, r=0.05, o=0.25 and T = 4/12 In(30/29)+(0.05+0.252 /2)×4/12 d = -= 0.4225 0.25 0.3333 d, In(30/29)+(0.05 -0.25? / 2)x4/12 = 0.2782 0.250.3333 N(0.4225) = 0.6637, N(0.2782) = 0.6096 N(-0.4225) = 0.3363, N(-0.2782) = 0.3904 a. The European call price is 30x0.6637 - 29e0.05x4/12 *0.6096 = 2.52 b. The American call price is the same as the European call price. It is $2.52. The Luropean pur price is
Can we use The Black-Scholes Formulas to calculate American calls? If can't, why the model answers said they are the same?
And how to find N(x) and N(-x) in the formula?
Question:-Can we use The Black-Scholes Formulas to calculate American calls?
Answer:-
Black-Scholes Formulas is to be used only on European option contracts and Not on Ameriacn option contracts.
In the given case it is given that the stock is a non dividend paying stock. In case of a call option on a non dividend paying stock, it will be Unwise for the option buyer to exercise his american call option before maturity.
Hence there will be no difference between the value of European and Americal call option for a Non dividend paying stock.
Non dividend paying stock will not fluctuate much. Hence it is assumed that the american call option holder will exercise only on the option maturity. Hence European and Americal call option for a Non dividend paying stock will be same under Black-Scholes Formulas.
Remember that Black-Scholes Model always assume that the Stock is Non dividend paying.
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Question:- How to find N(x) and N(-x) in the formula?
Answer:-
N(X) means the Cumulative standard Normal distribution Function.
It can be calculated in Excel by using ''NORM.DIST'' Function.
N(-x) = 1- N(X)
please see the attached file for the complete solution
