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Rebecca is interested in purchasing a European call on a hot new​ stock, Up, Inc. The call has a strike price of $98.00 and expires in 87 days. The current price of Up stock is

$124.63​, and the stock has a standard deviation of 45% per year. The​ risk-free interest rate is 6.56% per year. Up stock pays no dividends. Use a​ 365-day year.

a. Using the​ Black-Scholes formula, compute the price of the call.

b. Use​ put-call parity to compute the price of the put with the same strike and expiration date.

​(Note​: Make sure to round all intermediate calculations to at least five decimal places.​)

​ a. Using the​ Black-Scholes formula, compute the price of the call.

The price of the call is ​$___________.​(Round to two decimal​ places.)

b. Use​ put-call parity to compute the price of the put with the same strike and expiration date.

The price of the put is ​$___________.​ (Round to two decimal​ places.)

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Jean Keeling
Jean KeelingLv2
28 Sep 2019

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Related questions

Q1. Put-call parity

Does put-call parity mean the put and the call option (of the same stock, with same expiration, with same strike price) have the same value/price?

If not, for put and call to have the same prices, what must be the relationship between the strike price and the current stock price?

Hint: Find the Apple option page from Yahoo Finance and look for the strike price where the call and put price are similar.

Q2.A European call option and a European put option on a stock both have the same strike price of $45 and expire in 6 months. Currently, the market call price is $10 and the put price is $6. The risk-free rate is 2% per annum, and the current stock price is $49. Identify the arbitrage opportunity open to the trader. All the interest rates are with continuous compounding.

Kevin examines both American- and European-style options that have the same stock, expiration date, and strike price. Kevin argues that the European-style option will be sold at a higher price than the American-style option.

A. Examine Kevin’s belief given that the stock closed at $40, has an exercise price of $42 on the put and call options, the one-year put option is $3, the Treasury bill is 4.5%, and it expires in one year.

B. Calculate the value of a European-style option given put-call parity.

C. Determine the impact on the call option if (i) there is a rise in volatility; (ii) there is an increase in interest rate; and (iii) the time of option expiration declines.

Please be more specific in your response. Thank you in advance!

Suppose a call on a stock with strike price X +1 costs $1 and a put on a stock with strike price X −1 and the same expiration date costs $1. Suppose the price of the stock on expiration date is given by ST . Find the payoff to the investor that holds both the call and the put described above as a function of ST , first ignoring for premia and then taking premia into account. Draw the payoffs you found on a graph with ST on the horizontal axis.(piece-wise function)

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