The document discusses option valuation concepts including:
1) Put-call parity, which states the relationship between European put and call options on the same underlying asset in terms of stock price, strike price, risk-free rate, and time to expiration.
2) Option strategies including straddles, which involve buying a put and call with the same strike price, and butterflies, which involve buying and selling calls with different strike prices. These strategies bet on variability in the underlying asset price.
3) Using a binomial model to value a European call option on a stock that can take on two possible future prices, and forming a risk-free hedge portfolio from the stock and option to derive the option price
The document discusses option valuation concepts including:
1) Put-call parity, which states the relationship between European put and call options on the same underlying asset in terms of stock price, strike price, risk-free rate, and time to expiration.
2) Option strategies including straddles, which involve buying a put and call with the same strike price, and butterflies, which involve buying and selling calls with different strike prices. These strategies bet on variability in the underlying asset price.
3) Using a binomial model to value a European call option on a stock that can take on two possible future prices, and forming a risk-free hedge portfolio from the stock and option to derive the option price
The document discusses option valuation concepts including:
1) Put-call parity, which states the relationship between European put and call options on the same underlying asset in terms of stock price, strike price, risk-free rate, and time to expiration.
2) Option strategies including straddles, which involve buying a put and call with the same strike price, and butterflies, which involve buying and selling calls with different strike prices. These strategies bet on variability in the underlying asset price.
3) Using a binomial model to value a European call option on a stock that can take on two possible future prices, and forming a risk-free hedge portfolio from the stock and option to derive the option price
The document discusses option valuation concepts including:
1) Put-call parity, which states the relationship between European put and call options on the same underlying asset in terms of stock price, strike price, risk-free rate, and time to expiration.
2) Option strategies including straddles, which involve buying a put and call with the same strike price, and butterflies, which involve buying and selling calls with different strike prices. These strategies bet on variability in the underlying asset price.
3) Using a binomial model to value a European call option on a stock that can take on two possible future prices, and forming a risk-free hedge portfolio from the stock and option to derive the option price
20.1 You own a call option on Intuit stock with a strike price of $40. The option will expire in exactly three months’ time. a) If the stock is trading at $55 in three months, what will be the payoff of the call? Payoff: $55-$40 = $15 b) If the stock is trading at $35 in three months, what will be the payoff of the call? Payoff: $0 as the price today is higher than in three months. c) Draw a payoff diagram showing the value of the call at expiration as a function of the stock price at expiration.
20.2 You happen to be checking the newspaper and notice an arbitrage opportunity. The current stock price of Intrawest is $20 per share and the one-year risk-free interest rate is 8%. A one year put on Intrawest with a strike price of $18 sells for $3.33, while the identical call sells for $7. Explain what you must do to exploit this arbitrage opportunity.
This arbitrage opportunity exist due to:
𝐾 (𝑠𝑡𝑟𝑖𝑘𝑒 𝑝𝑟𝑖𝑐𝑒) 𝐶𝑎𝑙𝑙(𝐾𝑗ø𝑝𝑠𝑜𝑝𝑠𝑗𝑜𝑛) > 𝑃(𝑆𝑎𝑙𝑔𝑠𝑜𝑝𝑠𝑗𝑜𝑛) + 𝑆ℎ𝑎𝑟𝑒(𝑝𝑟𝑖𝑠𝑒𝑛 𝑝å 𝑢𝑛𝑑𝑒𝑟𝑙𝑖𝑔𝑔𝑒𝑛𝑑𝑒 𝑎𝑘𝑡𝑖𝑣𝑎) − (1+𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒) = 𝐶 $18 $7 > $3. 33 + $20 − (1+0.08) = $6, 66 As seen, the call is overpriced compared to the portfolio of the put, stock and risk-free borrowing. To exploit this arbitrage opportunity, I must sell the call option and buy the put, stock and borrow $16,67 which will give a net amount of $3.34 and no cash flow when the option expires.
20.3 Wesley Corp. stock is trading for $27/share. Wesley has 20 million shares outstanding and a market debt-equity ratio of 0.49. Wesley’s debt is zero-coupon debt with a 5-year maturity and a yield to maturity of 11%. a) Describe Wesley’s equity as a call option. What is the maturity of the call option? What is the market value of the asset underlying this call option? What is the strike price of this call option? Maturity of the call option: 5 years Market value of the asset underlying this call option = E + D = $27 * 20 + 0, 49 * $27 * 20 = $804, 6 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 Strike price of this call option = D = 0. 49 * $27 * 20 = $264, 6 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 b) Describe Wesley’s debt using a call option. Buy firm’s assets and short the equity call option. c) Describe Wesley’s debt using a put option. Can be described as a long risk-free debt with a five year maturity and short a put option on Wesley’s assets.
Chapter 21 - Option Valuation
21.1 The current price of Natasha Corporation stock is $6. In each of the next two years, this stock price can either go up by $2.50 or go down by $2. The stock pays no dividends. The one-year risk-free interest rate is 3% and will remain constant. Using the Binomial Model, calculate the price of a two-year call option on Natasha stock with a strike price of $7. 21.2 Eagletron’s current stock price is $10. Suppose that over the current year, the stock price will either increase by 100% or decrease by 50%. Also, the risk-free rate is 25% (EAR). a) What is the value today of a one-year at-the-money European put option on Eagletron stock? Pu=0 Pd=5 0−5 1 Delta = 20−5 =− 3 5−5(−1/3) B= 1,25 = 5, 33 P = -⅓*10 + 5,33 = $2.00
b) What is the value today of a one-year European put option on Eagletron stock with a strike price of $20? Pu=0 Pd=15 As seen these payoffs are three times the previous payoff of 5, which means that the put is worth 3*$2 = $6 c) Suppose the put options in parts a and b could either be exercised immediately, or in one year. What would their values be in this case? Exercised immediately: In a) Intrinsic value: $0, not relevant -> Value=$2
In b) Intrinsic value = $20-$10 = $10. Hence, it is better to exercise now as value is $10 and not $6 as in one year.
21.3 Rebecca is interested in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of $100 and expires in 90 days. The current price of Up stock is $120, and the stock has a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year. a) Using the Black-Scholes formula, compute the price of the call. 𝐶 = 𝑆 * 𝑁(𝑑1) − 𝑃𝑉(𝐾) * 𝑁(𝑑2)
𝑁(𝑑1) = 0,861 𝑁(𝑑2) = 0,813 𝐶 = 𝑆 * 𝑁(𝑑1) − 𝑃𝑉(𝐾) * 𝑁(𝑑2) = 120 * 0, 861 − 98, 53 * 0. 813 = $23, 21 b) Use put-call parity to compute the price of the put with the same strike and expiration date. 𝑃 = 𝐶 + 𝑃𝑉(𝐾) − 𝑆 = $23, 21 + $98, 53 − $120 = $1, 74
Exam Question - Task 1 Resit 2018
a) Explain the concept of Put-Call Parity using both the formula and by plotting the payoffs as a function of the stock price b) Option traders often refer to “straddles” and “butterflies”. Straddle: buy call with exercise price of $100 and simultaneously by put with exercise price of $100. Butterfly: Simultaneously buy one call with exercise price of $100, sell two calls with exercise price of $110, and buy one call with exercise price of $120. i) Draw position diagrams for the straddle and the butterfly, showing the payoffs from the investor’s net position. ii) Each strategy is a bet on variability. Explain Briefly the nature of this bet. c) A stock’s current price is $160, and there are two possible prices that may occur next period: $150 or $175. The interest rate on risk-free investments is 6% per period. Assume that a (European) call option exists on this stock having an exercise price of $155. i) How could you form a portfolio based on the stock and the call so as to achieve a risk-free hedge? ii) Compute the price of the call. iii) What would change if the exercise price was $180?
