Questions and Answers of Derivative Pricing

Determine which, if any, of the following positions has or have an unlimited loss potential from adverse price movements in the underlying asset, regardless of the initial premium received.I. Short 1
Aaron has purchased a forward contract on a stock. You are given:(i) If the stock price at expiration is S, his payo would be –$5.(ii) If the stock price at expiration is 1.1S, his payoff would be
You buy a 50-strike 6-month call option on a stock at a price of 5. The continuously compounded risk-free interest rate is 5%.At the end of 6 months, the profit from the long call option is
The market price of Stock A is 50. A customer buys a 50-strike put contract on Stock A for 500. The put contract is for 100 shares of A. Calculate the customer's maximum possible loss.(A) 0(B) 5(C)
You are given:(i) The current price of a 100-strike 9-month European put option is 12.(ii) A 9-month forward has a forward price of 105.(iii) The continuously compounded risk-free interest rate is
Stock XYZ has the following characteristics:• The current price is 40.• The price of a 35-strike 1-year European call option is 9.12.• The price of a 40-strike 1-year European call option is
You are given the following information about two options, A and B:(i) Option A is a one-year European put with exercise price 45.(ii) Option B is a one-year American call with exercise price
Jack buys a 50-strike 6-month European call option on stock ABC at a price of 8. Rose buys a 50-strike 6-month European put option on the same stock at a price of 6. The continuously compounded
Investor A wrote a 104-strike 1-year call option whose price is 2. Investor B entered into a 1-year long forward with a forward price of 105.The continuously compounded risk-free interest rate is
An investor purchased Option A and Option B for a certain stock today, with strike prices 70 and 80, respectively. Both options are European one-year put options.Determine which statement is true
Bob writes a two-year 100-strike European put with a premium of $10. The continuously compounded risk-free interest rate is 4%.Calculate the difference between Bob's maximum profit and his minimum
Comparing the profits of three puts) You are given the following premiums of one-year European put options on stock ABC for various strike prices:The effective annual risk-free interest rate is 8%.
The current price of a stock is 80. Both call and put options on this stock are available for purchase at a strike price of 65.Determine which of the following statements about these options is
Once upon a time, Leo entered into three separate positions involving 2-year options on the same stock.• Option I was a short American-style call with strike price 30.• Option II was a long
For a certain stock, Investor A purchases a 45-strike call option while Investor B purchases a 135-strike put option. Both options are European with the same expiration date. Assume that there are no
Several years ago, John bought three separate 6-month options on the same stock.• Option I was an American-style put with strike price 20.• Option II was a Bermudan-style call with strike price
Determine which of the following statements about a long European call option and a short European put option on the same underlying asset is/are correct.I. Both are long with respect to the
A customer buys a 50-strike put on an index when the market price of the index is also 50. The premium for the put is 5. Assume that the option contract is for an underlying 100 units of the index.
An investor purchased Call X and Call Y for a certain stock today, with strike prices 50 and 60, respectively. Both options are European options with the same time to expiration.Determine which of
Consider a European put option on a stock index without dividends, with 6 months to expiration and a strike price of 1,000. Suppose that the annual nominal risk-free rate is 4% convertible
The price of an asset will either rise by 25% or fall by 40% in 1 year, with equal probability. A European put option on this asset matures after 1 year.Assume the following:• Price of the asset
A nondividend-paying stock currently sells for 100. One year from now the stock sells for 110. The continuously compounded risk-free interest rate is 6%. A trader purchases the stock in the following
The dividend yield on a stock and the interest rate used to discount the stock's cash flows are both continuously compounded. The dividend yield is less than the interest rate, but both are
A certain stock costs 40 today and will pay an annual dividend of 6 for the next 4 years. An investor wishes to purchase a 4-year prepaid forward contract for this stock. The first dividend will be
Determine which of the following is NOT a distinguishing characteristic of futures contracts, relative to forward contracts. (A) Contracts are settled daily, and marked-to-market. (B) Contracts are
For t ≥ 0, let S(t) be the time-t price of Stock ABC. You are given:(i) S(0) = 100(ii) At time 0.5, a cash dividend of $10 per share will be paid.(iii) From time 0.75 to time 1, dividends are paid
A one-year forward contract on a stock has a price of $75. The stock is expected to pay a dividend of $1.50 at two future times, six months from now and one year from now, and the annual effective
Determine which of the following statements about futures and forward contracts is false.(A) Frequent marking-to-market and settlement of a futures contract can lead to pricing differences between a
An investor enters a long position in a futures contract on an index (F) with a notional value of 200 × F, expiring in one year. The index pays a continuously compounded dividend yield of 4%, and
The current price of stock XYZ is $80. A one-year forward contract on stock XYZ has a price of $84. Stock XYZ is expected to pay a dividend of $2 six months from now and a dividend of $3 one year
You are given the following information about Stock XYZ:(i) The current price of the stock is 35 per share.(ii) The expected continuously compounded rate of return is 8%.(iii) The stock pays
Judy decides to take a short position in 20 contracts of S&P 500 futures. Each contract is for the delivery of 250 units of the index at a price of 1500 per unit, exactly one month from now. The
The current price of a stock is 100. The stock pays dividends continuously at a rate proportional to its price. The dividend yields is 3%. The continuously compounded risk-free interest rate is 7%.
The following relates to one share of XYZ stock:• The current price is 100.• The forward price for delivery in one year is 105.• P is the expected price in one year.Determine which of the
The current price of a medical company's stock is 75. The expected value of the stock price in three years is 90 per share. The stock pays no dividends.You are also given:(i) The risk-free interest
The current price of a stock is 200, and the continuously compounded risk-free interest rate is 4%. A dividend will be paid every quarter for the next 3 years, with the first dividend occurring 3
It is now January 1, 3018. You are given: (i) The current price of the stock is 1,000. (ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield changes
Determine which of the following positions has the same cash ows as a short stock position.(A) Long forward and long zero-coupon bond (B) Long forward and short forward (C) Long forward and short
The current price of stock XYZ is 120. Stock XYZ pays dividends continuously at a rate proportional to its price. The dividend yield is 4%. The continuously compounded risk-free interest rate is 6%.
A market maker in stock index forward contracts observes a 6-month forward price of 112 on the index. The index spot price is 110 and the continuously compounded dividend yield on the index is 2%.The
The current price of a nondividend-paying stock is 100. The annual effective risk-free interest rate is 4%, and there are no transaction costs.The stock's two-year forward price is mispriced at 108,
(i) The current price of a stock is 1,000.(ii) The stock pays dividends continuously at a rate proportional to its price.(iii) The continuously compounded risk-free interest rate is 5%.(iv) A 6-month
You short sold 100 shares of stock X on November 1, 3016 and closed your position on November 1, 3018. You are given:(i) Stock X pays dividends continuously at a rate proportional to its price. The
The current stock price is 80. A dividend of 2 will be paid 6 months from now. The continuously compounded risk-free interest rate is 6%.If you observe a 1-year forward price of 82, describe actions
Investors in a certain stock demand to be compensated for risk. The current stock price is 100. The stock pays dividends at a rate proportional to its price. The dividend yield is 2%. The
Consider a stock which pays dividends continuously at a rate proportional to its price. The dividend yield is less than the interest rate, but both are positive and continuously compounded.Rank the
You observe two prices $65.1 and $65.2 quoted in the market for the stock of Company ABC.The brokerage commission includes:(i) 0.3% of the transaction amount(ii) A fixed cost of $50 per
You are given the following information: (i) The current bid price and ask price of stock X are 50 and 51, respectively. (ii) A dividend of 3 will be paid 6 months from now. (iii) The continuously
The ask price for a share of ABC company is 100.50 and the bid price is 100. Suppose an investor can borrow at an annual effective rate of 3.05% and lend (i.e., save) at an annual effective rate of
You are given the following historical futures prices of the P&K 689 Index observed at different time points for various maturities:On March 1, 2018, Cyrus decides to take a long position in ten
You are given the following information: (i) The current bid price and ask price of stock Y are 40 and 41, respectively. (ii) Stock Y pays dividends continuously at a rate proportional to its
The P&Q futures is currently trading at 1,629. The P&Q index pays dividends continuously at a rate proportional to its price. The dividend yield is 2%. Today Peter enters into eight 3-month P&Q long
In Figure 3.4.1, identify all possible asset price(s) at expiration such that the profit of a long K-strike straddle is zero.Figure 3.4.1 -FVO,T[C(K) + P(K)] K Payoff Profit S(T)
You enter into a long synthetic forward on a stock using 1-year European options. The price of a 50-strike call option is 6.8 and the price of a 50-strike put option is 4.2. The continuously
Student A constructs a K1-K2 bull spread using call options, while Student B constructs a K1-K2 bull spread using put options. All options are European with the same underlying asset and time to
Determine whether each of the following positions has an unlimited loss potential from adverse price movements in the underlying asset, regardless of the initial premium received.(A) Long forward(B)
Determine which of the following risk management techniques can hedge the financial risk of an oil producer arising from the price of the oil that it sells.I. Short forward position on the price of
Assume that a single stock is the underlying asset for a forward contract, a K-strike call option, and a K-strike put option.Assume also that all three derivatives are evaluated at the same point in
An investor bought a 70-strike European put option on an index with six months to expiration. The premium for this option was 1.The investor also wrote an 80-strike European put option on the same
You are given the following information:(i) The current price of the stock is 45 per share.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is
A producer of gold has expenses of 800 per ounce of gold produced. Assume that the cost of all other production-related expenses is negligible and that the producer will be able to sell all gold
You buy a stock at $300 and buy an at-the-money 9-month European put option on the stock at a price of $15.The continuously compounded risk-free interest rate is 5%.Calculate your 9-month profit if
The PS index has the following characteristics:• One share of the PS index currently sells for 1,000.• The PS index does not pay dividends.Sam wants to lock in the ability to buy this index in
The current price of a nondividend-paying stock is 40 and the continuously compounded risk-free interest rate is 8%. The following table shows call and put option premiums for three-month European
You are given:(i) The current price of a stock is 70.(ii) The continuously compounded risk-free interest rate is 5%.(iii) The price of a 70-strike 1-year European call option is 5.(iv) The price of a
A trader shorts one share of a stock index for 50 and buys a 60-strike European call option on that stock that expires in 2 years for 10. Assume the annual effective risk-free interest rate is 3%.
You are selecting among various put options with different strike prices to hedge a long asset position.Which of the following statements is true? Give your reasoning.(A) Higher-strike puts cost more
For each ton of a certain type of rice commodity, the four-year forward price is 300. A four-year 400-strike European call option costs 110. The annual risk-free force of interest is a constant
The current price for a stock index is 1,000. The following premiums exist for various options to buy or sell the stock index six months from now:Strategy I is to buy the 1,050-strike call and to
In the Midterm Exam of your favorite derivatives pricing course, a really “clever” student erroneously constructed a K1-K2 strangle by using in-the-money options. Specifically, he bought a call
Supway is a sandwich shop, one of its main production inputs being wheat.Determine whether each of the following risk management techniques can hedge the financial risk faced by Supway arising from
Consider an airline company that faces risk concerning the price of jet fuel. Select the hedging strategy that best protects the company against an increase in the price of jet fuel.(A) Buying calls
XYZ stock pays no dividends and its current price is 100.Assume the put, the call and the forward on XYZ stock are available and are priced so there are no arbitrage opportunities. Also, assume there
Joe believes that the volatility of a stock is higher than indicated by market prices for options on that stock. He wants to speculate on that belief by buying or selling at-the-money
Box spreads are used to guarantee a fixed cash flow in the future. Thus, they are purely a means of borrowing or lending money, and have no stock price risk.Consider a box spread based on two
Assume the same underlying stock, same time to expiration, and same strike price for all derivatives in this problem.Which of the following must have the same profit as a floor coupled with a cap?
Stock ABC has the following characteristics:• The current price to buy one share is 100.• The stock does not pay dividends.• European options on one share expiring in one year have the
Determine which of the following statements about options is true. (A) Naked writing is the practice of buying options without taking an offsetting position in the underlying asset. (B) A covered
CornGrower is going to sell corn in one year. In order to lock in a fixed selling price, CornGrower buys a put option and sells a call option on each bushel, each with the same strike price and the
The following table shows 1-year European call and put option premiums at two strike pricesThe continuously compounded risk-free interest rate is 6%. Describe actions you could take to construct an
Assume the same underlying stock, same time to expiration, and same strike price for all derivatives in this problem.Which of the following must have the same profit as a floor coupled with a written
An investor has written a covered call. Determine which of the following represents the investor’s position.(A) Short the call and short the stock(B) Short the call and long the stock(C) Short the
The current price of a nondividend-paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You are given that the price of a 35-strike call option is 3.35 higher than the
Consider the following investment strategy involving put options on a stock with the same expiration date.(i) Buy one 25-strike put(ii) Sell two 30-strike puts(iii) Buy one 35-strike putCalculate the
Determine which of the following strategies creates a ratio spread, assuming all options are European.(A) Buy a one-year call, and sell a three-year call with the same strike price.(B) Buy a one-year
The current price of a nondividend-paying stock is 1,000 and the continuously compounded risk-free interest rate is 5%. Richard wants to lock in the ability to sell a unit of this stock in six months
Assume the same underlying asset, same time to expiration, and same strike price for all concerned options. Which of the following must have the same profit as a written covered call?(A) Short
An investor is analyzing the costs of two-year, European options for aluminum and zinc at a particular strike price.For each ton of aluminum, the two-year forward price is 1400, a call option costs
The payoff diagram of a certain investment strategy involving 2- year European put options on a stock is shown on the right.You are given: (i) (ii) The continuously compounded risk-free interest
The current price of a nondividend-paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You enter into a short position on 3 call options, each with 3 months to maturity,
The current price of a stock is 100, and the continuously compounded risk-free interest rate is 10%. A $2.5 dividend will be paid every quarter, with the first dividend occurring 2 months from
An investor has a long position in a nondividend-paying stock, and, additionally, has a long collar on this stock consisting of a 40-strike put and 50-strike call. Determine which of these graphs
You are given:(i) The price of a nondividend-paying stock is $31.(ii) The continuously compounded risk-free interest rate is 10%.(iii) The price of a 3-month 30-strike European call option is $3.(iv)
The current price of a nondividend-paying stock is 60 and the continuously compounded risk-free interest rate is 6%.Actuary A writes a 1-year 70-strike call option whose price is 1.50. Actuary B
You are given that one-year 15-strike European call and put premiums on a share of Iowa Inc. are 6.46 and 0.75, respectively. The stock pays dividends continuously at a rate proportional to its
Stock X pays dividends continuously at a rate proportional to its price. The dividend yield is 2%. You are given the following option prices for European puts and calls, all written on stock X and
Determine which of the following statements about a long stock and a long K1-K2 collared stock is/are always correct.I. Both are long with respect to the underlying stock.II. The long collared stock
The current price of stock ABC is 40. Stock ABC pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.You are given the following premiums of one-year European
Farmer Brown grows wheat, and will be selling his crop in 6 months. The current price of wheat is 8.50 per bushel. To reduce the risk of fluctuation in price, Brown wants to use derivatives with a
Happy Jalapenos, LLC has an exclusive contract to supply jalapeno peppers to the organizers of the annual jalapeno eating contest. The contract states that the contest organizers will take delivery

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