Questions and Answers of Derivative Pricing

A particular market was served by two products offered by Acme and a competitor.The prices and quality ratings of the two products are as follows:Price Quality rating Acme brand $2.00 50 Competitor
Giffen good. A penurious graduate student has a food budget of $100.00/week. To survive with sufficient energy to attend classes, he knows that he needs to consume 50 protein units per week. The only
Table 13.5 shows the take-up probability predicted by two different bid-response models and the actual outcome of 10 historical bids for a telecommunications company.a. What are the RMSE,
The printer cartridge manufacturer with the data shown in Table 13.3 has used historical data to estimate the coefficients in the model in Equation 13.11 and has come up with the model ρ(p, x) = a +
HP is bidding against Lenovo for an order of 150 laptops. HP’s unit cost is $1,000 per laptop, and, based on previous experience, HP’s belief is that Lenovo’s bid will be uniformly distributed
The questions in this problem are variations on Example 12.4. The best way to answer them is to build a spreadsheet model that calculates the revenue for the different policies under different
Consider a seller who wants to sell a product in two periods when all customers are strategic: they all fully anticipate the actions of the seller and choose to purchase in the first period, wait to
A department store has 700 pairs of purple capri stretch pants that it must sell in the next four weeks. The store manager knows that demand by week for the next four weeks will be linear, with the
Now extend the two-period markdown model in Section 12.1.1 to the case where customers have a lower willingness to pay for the good in the second period. Specifically, assume that each customer’s
Extend the two-period markdown model in Section 12.1.1 to three periods. That is, assume that the price-response function is d(p) = 1,000 – 100p, marginal cost is 0, and customers purchase as soon
In Example 11.2, what is the minimum value of the overbooking penalty D that would be required for the expected revenue change from overbooking by one seat to be less than 0?
A rental car company will have 100 cars available for rent on a particular day. It expects that demand for that day will be very high, so demand is certain to be higher than 300 bookings. If it
A low-cost airline sells only nonrefundable tickets. Customers pay in full at the time of booking. If they cancel or miss their flight for any reason, no portion of the price is refunded, and they
A flight has 100 seats and a passenger fare of $130. The denied-boarding cost is$390 per denied boarding, and the no-show rate is 0.16. Demand for this flight is extremely high; in fact, for any
Capacity, fare, denied-boarding cost, and the no-show distribution are the same as in Exercise 2. However, there is now a 0.6 probability that there will be a walk-up customer for the flight.
A flight has 100 seats and a passenger fare of $130. The number of no-shows is independent of total bookings and is given by a normal distribution with a mean of 22 and a standard deviation of 15.
Solve the decision tree in Figure 11.6 to determine a formula for the total booking limit that maximizes expected net revenue when there is a no-show penalty of αp.Does the no-show penalty generally
CU Airlines operates two flights, one from New York to Phoenix and another one from Phoenix to San Francisco. It sells a full fare and a discount fare for each leg, and a single fare for the combined
In Example 10.1, determine which bookings would be accepted using the greedy heuristic and the corresponding system revenue. What was the percentage improvement in revenue from optimizing the network?
The airline offering the flights and fares shown in Table 10.4 decides to raise the San Francisco–to–St. Louis discount fare from $170 to $225. It estimates that discount demand at this new fare
Consider an airline with a single hub in the Midwest. Ten flights arrive from cities in the West at the hub every day and connect with nine flights departing for cities in the East. How many products
How many products can Amtrak offer on the California Zephyr, assuming a single fare class? (Remember that every combination of possible boarding and deboarding stations defines a different product.)
Senilria Airlines has started a new flight from Rome to Palermo, Sicily, once a week on Monday mornings and has operated the flight for the last 12 weeks. Senilria offers three booking classes on the
Granite State Airlines also serves the route between Washington, D.C. (Reagan), and Portsmouth, New Hampshire, with a single flight daily. The airline sells both discount-fare and full-fare tickets.
Granite State Airlines serves the route between New York and Portsmouth, New Hampshire, with a single-flight-daily 100-seat aircraft. The one-way fare for discount tickets is $100, and the one-way
Roll back the decision tree in Figure 9.7 to determine a formula for the period 3 booking limit that would maximize expected net revenue given the displacement probabilities q1 and q2.
A restaurant has 25 tables, each of which can seat up to four people. Typically, it can do three seatings per table during the dinner period from 6:00 to 10:00 p.m. The restaurant has a fairly
The popular ride-sharing app Lyber has determined that the general form of rider response to its price multiplier p is given by the logit formula d p ee( )=( – )( – ) D a bp a bp 1.Here, D is the
The popular a cappella choral group Here Comes Treble is coming to Columbia University for a concert. The concert will be in Lerner Auditorium, which has C seats. Customers can be segmented into
The theme park owner performs some market research and determines that his customers can best be represented by the following model.i. Base customer demand for each day of the week is linear and is
Assume that the theme park owner invested in expanding his park so that he could accommodate up to 1,500 customers each day.a. What single price would maximize his total revenue, assuming he faces
The optimal variable prices for theme park admission in Table 7.5 are based on the assumption that admission fees are the only source of revenue for the park. However, the owner determines that
A barber charges $12 per haircut and works Saturday through Thursday. He can perform up to 20 haircuts a day. He currently performs an average of 12 haircuts per day during the weekdays (Monday
Ancillary Revenue. Stanford Stadium has been repaired so that it again seats 60,000 people. Now assume that, on average, each member of the general public will consume $20 worth of concessions,
An earthquake damages Stanford Stadium so that only 53,000 seats are available for the Big Game. What is the optimal single price and the total revenue? What are the optimal separate prices to charge
Let us return to the Stanford Stadium pricing problem in Section 7.4, assuming a capacity of 60,000 seats and the price-response functions for students and for the general public as given in
For the single-customer demand function specified by Equation 6.1, what is the corresponding hazard rate and price elasticity? What do they imply about the price calculated in Equation 6.2?
Assume that it costs Budget $20 per day for every car it rents out, regardless of model. What is the implied price elasticity of customers for each of the first five car types listed in Table 6.3?
Arbitrage. A supplier is selling hammers in two cities, Pleasantville and Happy Valley. It costs him $5.00 per hammer delivered in each city. Let p1 be the price of hammers in Pleasantville and p2 be
Frank owns a hot-dog stand. It costs him $1 to make each hot dog and he faces a linear price-response function d(p) = (100 – 8p)+ for each day.a. Find Frank’s contribution-maximizing price and
An auto manufacturer can manufacture compact cars for an incremental cost of$5,000 apiece. She faces a logit price-response function for sales in the next month, with parameters C = 40,000, b =
A retailer is currently charging a price of $147.52 for a Hewlett-Packard OfficeJet printer that costs him $112.00 per unit. He determines that the point price elasticity of this model of printer is
Consider a seller seeking to maximize contribution. Under what relative values of his current price p, his costc, and his point elasticity (p) should the seller raise his price to increase
Fit a logistic model to the test data in Table 4.3 using Price, Weekend, and Potential Demand as explanatory variables.a. What are the coefficients for each explanatory variable?b. Calculate RMSE,
For the three price-response functions listed in Table 4.4—linear, exponential, and constant-elasticity—fit a model on the training data in Table 4.2 that includes Weekend as an explanatory
The average ticket prices for concerts held by six different artists in 2018 were as follows:8 Artist Ticket price Bruno Mars $176.67 The Eagles $159.10 The Rolling Stones $155.26 Jay Z/Beyoncé
Brain and Company is a consulting group that offers a foolproof pricing and revenue optimization service guaranteed to deliver $2 million in benefit to a customer. It costs Brain and Company $500,000
Assume the Black-Scholes framework. You are given:(i) The current stock price is 95.(ii) The stock’s volatility is 10%.(iii) The stock pays dividends continuously at a rate proportional to its
Assume the Black-Scholes framework. Let S(t) denote the price at time t of a stock, which will pay a dividend of $1 after 3 months.Consider a European gap option which matures in 9 months. If the
Michael has ordered a Rolls Royce car for 200,000 British pounds, which he will pay when the car is delivered to him in three months. Because Michael has got an A+ in ACTS:4830 from the devilish
Consider a “sad” 1-year European contingent claim on a stock. You are given:(i) The time-0 stock price is 70.(ii) The stock pays dividends continuously at a rate proportional to its price. The
Assume the Black-Scholes framework. For t ≥ 0, let S(t) denote the time-t price of a stock. Consider a 1-year European contingent claim. If the 1-year stock price is less than $60, the payoff of
Assume the Black-Scholes framework. For a stock which pays dividends continuously at a rate proportional to its price, you are given:(i) The continuously compounded expected rate of stock-price
Assume the Black-Scholes framework. For a stock which pays dividends continuously at a rate proportional to its price, you are given:(i) The probability that a 3-month 70-strike 75-trigger European
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:(i) S(0) = 65.(ii) The stock pays dividends continuously at a rate proportional to its price.
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:(i) S(0) = $48.(ii) The stock pays dividends continuously at a rate proportional to its price.
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock that pays dividends continuously at a rate proportional to its price.Consider a 1-year European gap option. If
You are given the following generic Black-Scholes-type pricing function:and all variables are positive. Your boss, who knows nothing about option pricing, has asked you to analyze the following
Assume the Black-Scholes framework. You are given:(i) The current stock price is 100.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.(iii) The
Assume the Black-Scholes framework. You are given the following information about two stocks:(i)(ii) The correlation between the continuously compounded returns on the two stocks is −0.3. (iii)
Assume the Black-Scholes framework. For a 5-month European gap put option on a nondividend-paying stock, you are given:(i) The current price of the stock is 120.(ii) The stock’s volatility is
Assume the Black-Scholes framework. Two actuaries, A and B, are computing the prices of a European call and a European put using different parameters.You are given:Describe the relationship between
Consider two nondividend-paying stocks whose time-t prices are denoted by S1(t) and S2(t), respectively.You are given:(i) S1(0) = S2(0) = 10.(ii) Stock 1’s volatility is 25%.(iii) Stock 2’s
Consider a European option to exchange Stock 2 for Stock 1 at a certain future date. Each stock pays dividends continuously at a rate proportional to its price.Determine whether each of the
For j = 1, 2, and t ≥ 0, let Sj(t) denote the price of one share of stock j at time t (in years). Both stocks pay no dividends.Let π be the current price of a 4-year European exchange option that
Assume the Black-Scholes framework. For j = 1, 2 and t ≥ 0, let Sj(t) denote the time-t price of Stock j.(a) Consider a T-year European contingent claim whose payoff is the maximum of the two
You are given:(i) The current prices of Stock 1 and Stock 2 are 100 and 200, respectively.(ii) Stocks 1 and 2 pay dividends continuously at a rate proportional to their prices. The dividend yield of
Consider a model with two nondividend-paying stocks, Stock 1 and Stock 2, and a special 5-year European straddle on Stock 1, with a strike price given by the 5-year price of Stock 2.You are given:(i)
You are given:(i) Stock XYZ pays no dividends.(ii) Derivative A gives its holder the right, but not the obligation, to buy an at-the-money European call option for $6 at the end of 6 months. The call
Assume the Black-Scholes framework. Consider two nondividend-paying stocks whose time-t prices are denoted by S1(t) and S2(t), respectively.You are given:(i) S1(0) = $100 and S2(0) = $150.(ii) Stock
Assume the Black-Scholes framework. For t ≥ 0, let S1(t) and S2(t) be the time-t prices of Stock 1 and Stock 2, respectively. You are given:(i) S1(0) = $100 and S2(0) = $120.(ii) The volatility of
Which of the following statements about exotic call options is/are correct?(A) The gamma of a European cash-or-nothing call option must be positive.(B) The vega of a European cash-or-nothing call
For a threeperiod binomial stock price model, you are given:(i) The length of each period is one year.(ii) The current price of a nondividend-paying stock is 100.(iii) u = 1.1, where u is one plus
You use the following information to construct a binomial forward tree for modeling the price movements of a stock:(i) The length of each period is 6 months.(ii) The current stock price is 100.(iii)
For t ≥ 0, let S(t) be the time-t price of a stock. You are given:(i) S(0) = 15.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.(iii) The
You use the following information to construct a binomial forward tree for modeling the price movements of a nondividend-paying stock:(i) The length of each period is 6 months.(ii) The current stock
You use the following information to construct a binomial forward tree for modeling the price movements of a stock:(i) The length of each period is 6 months.(ii) The current stock price is 100.(iii)
You use the following information to construct a binomial forward tree for modeling the movements of the dollar/euro exchange rate:(i) The length of each period is 3 months.(ii) The current
Consider the following European options having the same strike price, time to maturity, and underlying stock:I. A plain vanilla call option II. A gap call option III. An extrema lookback call
For a binomial model for the price of a nondividend-paying stock, you are given:(i) The length of each period is 1 year.(ii) The current price of the stock is 120.(iii) u = 1.15, where u is one plus
For a binomial tree modeling the price movements of a nondividend-paying stock, you are given:(i) The length of each period is 4 months.(ii) The current stock price is 120.(iii) u = 1.2212, where u
Consider the following up-and-in 60-strike European call options on the same underlying stock with the same time to expiration:The current price of the stock is 50.Rank the four barrier options, from
Assume the Black-Scholes framework. You are given:(i) The current price of a nondividend-paying stock is 80.(ii) The stock’s volatility is 30%.(iii) The continuously compounded risk-free interest
Assume the Black-Scholes framework. You are given:(i) The current stock price is 40.(ii) The stock pays no dividends.(iii) The stock’s volatility is 30%.(iv) The continuously compounded risk-free
For a binomial stock price model, you are given:(i) The length of each period is 1 year.(ii) The current price of a nondividend-paying stock is 100.(iii) u = 1.15, where u is one plus the percentage
For a four-period binomial stock price model, you are given:(i) The length of each period is 3 months.(ii) The current price of a nondividend-paying stock is 100.(iii) u = 1.11.(iv) d = 0.90.(v) The
You use the following information to construct a binomial forward tree for modeling the price movements of a stock:(i) The length of each period is 1 year.(ii) The current stock price is 200.(iii)
Consider a chooser option (also known as an as-you-like-it option) on stock ABC. At time τ (in years) with 0 You are given:(i) The current price of stock ABC is 32.(ii) Dividends of 1.5 are paid at
Assume the Black-Scholes framework. Consider a special chooser option (also known as an as-you-like-it option) on a nondividend-paying stock. One year from now, its holder will choose whether it
Consider a chooser option (also known as an as-you-like-it option) on a nondividend-paying stock.At time 1, its holder will choose whether it becomes a European call option or a European put option,
Consider a chooser option (also known as an as-you-like-it option) on two stocks. At time 1, its holder will choose whether it becomes a European option to exchange two units of Stock B for one unit
The current time is t = 0 (in years). Assume the Black-Scholes framework. You are given:(i) The current stock price is 40.(ii) The stock’s volatility is 40%.(iii) The stock pays dividends
Assume the Black-Scholes framework. Let S(t) be the time-t price of a stock. Consider a special 3-year European contingent claim which pays a certain amount three years from now, provided that S(3)
Assume the Black-Scholes framework. Consider a special forward start option which, 1 year from today, will give its owner a 1-year European put option with a strike price equal to the one-year stock
Assume the Black-Scholes framework. Consider a special forward start option which, 2 years from today, will give its owner a 1-year 100-strike European gap call option whose payment trigger is equal
You are given:(i) The current price of a stock is 100.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 1%.(iii) The continuously compounded
Assume the Black-Scholes frame-work. For t ≥ 0, let S(t) be the time-t price of a stock.You are given:(i) S(0) = 20.(ii) The stock’s volatility is 25%.(iii) The stock pays dividends continuously
Assume the Black-Scholes framework. Three months ago, Embryo (Ambrose’s twin brother) bought a 1-year 50-strike European cash-or-nothing call option of $1,000 on a nondividend-paying stock. He
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:(i) S(0) = 100.(ii) The stock’s volatility is 25%.(iii) The stock pays dividends continuously
This problem shows how the pricing formula for a T-year K-strike European cash-or-nothing call option of $1 can be retrieved from that of a plain vanilla T-year K-strike European call option.(a)

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