Question

Suppose that you are holding a European call option on General Motors stock that expires in 5 years. The option is currently at-the-money. GM's current stock price is $42.50 and the current yield on a 5-year Treasury bond is 2%. The standard deviation of returns on GM stock is 25%. For the purposes of this series of questions, you should assume that GM does not pay dividends.

You may assume that all of the information above applies.

What is the Black-Scholes value of the European call? (Hint: you may use the spreadsheet that we considered in Week 6 to help you answer this question. Please express your answer to the nearest cent.)

Given your answer to the previous question, what is the value of a European put option on GM stock that expires in 5 years and is also currently at-the-money? (Please express your answer to the nearest cent.)

Suppose that the current price of GM stock were $50 instead of $42.50, but the strike price of the options, the time to expiration, the risk-free rate, and the volatility of returns on GM stock were all the same. How would the values of the put and call option change? Provide a clear explanation for why the values move in the direction that you propose. (No additional calculations are necessary for this problem.)

Answer 1

Black Scholes Formula For finding out option pricings:

Excel working

b) For Put Formula is :

excel working:

c) When stock price change to $ 50

you just have to change the Stock price and calculation will be as follows:

as you can see the call option price has increased and put one has decreased due to stock price upward movement.

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