# What is a replicating portfolio?

1. What is a financial option? What is the single most important characteristic of an option?
2. Options have a unique set of terminology.

Define the following terms: (1) Call option (2) Put option (3) Strike price or exercise price (4) Expiration date (5) Exercise value (6) Option price (7) Time value (8) Writing an option (9) Covered option (10) Naked option (11) In-the-money call (12) Out-of-the-money call (13) LEAPS Copyright 2020 Cengage Learning.

1. C) Consider Triple Play’s call option with a \$25 strike price. The following table contains historical values for this option at different stock prices: Stock Price \$25 30 35 40 45 50 Call Option Price \$ 3.00 7.50 12.00 16.50 21.00 25.50

(1) Create a table that shows

(a) stock price,

(b) strike price,

(c) exercise value,

(d) option price, and

(e) the time value, which is the option’s priceless its exercise value.

(2) What happens to the time value as the stock price rises? Why? d. Consider a stock with a current price of P 5 \$27. Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 0.71. Consider a call option on the stock with a strike price of \$25 that expires in 6 months. The risk-free rate is 6%.

(1) Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option?

(2) Suppose you write one call option and buy Ns shares of stock. How many shares must you buy to create a portfolio with a riskless payoff (i.e., a hedge portfolio)? What is the payoff of the portfolio?

(3) What is the present value of the hedge portfolio? What is the value of the call option?

(4) What is a replicating portfolio? What is arbitrage?

1. In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM).

(1) What assumptions underlie the OPM?

(2) Write out the three equations that constitute the model.

(3) According to the OPM, what is the value of a call option with the following characteristics? Stock price 5 \$27.00 Strike price 5 \$25.00 Time to expiration 5 6 months 5 0.5 years Risk-free rate 5 6.0% Stock return standard deviation 5 0.49

1. What impact does each of the following parameters have on the value of a call option?

(1) Current stock price

(2) Strike price

(3) Option’s term to maturity

(4) Risk-free rate

(5) Variability of the stock price g. What is put-call parity?

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