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derivative pricing

Questions and Answers of Derivative Pricing

You are given:(i) An investor short-sells a nondividend-paying stock that has a current price of 44 per share.(ii) This investor also writes a collar on this stock consisting of a 40-strike European
Let C(K) and P(K) be the premiums of three-month K-strike European call and put options on the same stock, respectively. You are given that |C(60) − C(65)| = 3 and the continuously compounded
Determine which statement about zero-cost purchased collars is FALSE.(A) A zero-width, zero-cost collar can be created by setting both the put and call strike prices at the forward price.(B) There
You are given the following information:(i) The current price of stock Y is 30.(ii) Dividends of 1 per unit of stock will be paid in two months and in eight months.(iii) The continuously compounded
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 option premiums for 3-month European options of
Determine whether each of the following strategies creates a long bear spread, assuming that all options are European and on the same underlying asset.(A) Buy a 45-strike call and sell a 50-strike
You are given that the price of a 70-strike call option is 8.3 and the price of a 80-strike call option is 2.7, where both options expire in one year and have the same underlying asset.The
The following table shows the premiums of European call and put options having the same nondividend-paying stock, the same time to expiration but different strike prices:An investor constructs a
An investor wrote a 45-strike European call option on an index with three years to expiration. The premium for this option was 4.The investor also bought a 55-strike European call option on the same
Consider a box spread based on two distinct strike prices K and L with K < L that is used to lend money, so that there is a positive cost to this transaction up front, but a guaranteed positive
The following table shows the prices of European call and put options with the same underlying asset, time to expiration, but different strike prices:Calculate the profit on a 17-23 long collared
You are given the following information about four European options on the same underlying asset:(i) The price of a 25-strike 1-year call option is 6.85.(ii) The price of a 35-strike 1-year call
The current price of a stock is 50. The stock will pay a single dividend of 0.75 in one month. The continuously compounded risk-free interest rate is 6%.The following table shows the premiums of
Apple expects to sell pork bellies 3 months from now. The current 3-month forward price for pork belly is 4 per ton. Apple has decided to buy a zero-cost collar to reduce his exposure to the price of
The payoff of a derivative contract maturing in one year is given bywhere S(1) is the one-year price of the underlying nondividend-paying stock. You are given:(i) The continuously compounded
Determine whether each of the following statements about zero-cost purchased collars on stocks is true or false. Assume that options at all positive strike prices are available for trading. Note that
The payoff of a special 1-year derivative on a nondividend-paying stock is described by the following piecewise linear function:where S(1) is the one-year price of the stock.You are given:(i) The
The stock of Iowa Actuarial Corporation has been trading in a narrow range around its current price of 45 per share for months. Dividends of 2 are payable quarterly, with the first dividend payable
The current price of stock ABC is 40. Stock ABC pays dividends continuously at a rate proportional to its price. The dividend yield is 3%. The continuously compounded risk-free interest rate is
The price of a stock has hovered around its current price of 70 for several months, but you believe that the stock price will break far out of that range over the next 4 months, without knowing
The current price of stock XYZ is 1,000, and the continuously compounded risk-free interest rate is 8%. A dividend will be paid at the end of every 2 months over the next year, with the first
Determine whether each of the following statements about butterfly spread is true or false.(A) A long butterfly spread is a bet on the volatility of the underlying asset being higher than that
The following table shows the premiums of European call and put options having the same underlying stock, the same time to expiration but different strike prices:You use the above call and put
The payoff diagram of an investment strategy involving 3-year European put options on a stock is shown below:You are given:(i)(ii) The continuously compounded risk-free interest rate is
A nondividend-paying stock, S, is modeled by the binomial tree shown below.A European call option on S expires at t = 1 with strike price K = 12.Calculate the number of shares of stock in the
Consider the following information about a European call option on stock ABC:• The strike price is $95.• The current stock price is $100.• The time to expiration is 2 years.• The continuously
Consider a 9-month dollar-denominated American put option on British pounds. You are given that:(i) The current exchange rate is 1.43 US dollars per pound.(ii) The strike price of the put is 1.56 US
Consider a 50-65 1-year strangle strategy. You are given:(i) The stock currently sells for $55.(ii) In one year, the stock will either sell for $70 or $45.(iii) The effective annual risk-free
For a two-period binomial model, you are given:(i) Each period is one year.(ii) The current price for a nondividend-paying stock is 20.(iii) u = 1.2840, where u is one plus the rate of capital gain
The price of a nondividend-paying stock is currently $50.00. It is known that at the end of two months, it will be either $54.00 or $46.00. The risk-free interest rate is 9.0% per annum with
You are to price options on a futures contract. The movements of the futures price are modeled by a binomial tree. You are given:(i) Each period is 6 months.(ii) u/d = 4/3, where u is one plus the
For a two-year European put option, you are given the following information:• The stock price is $35.• The strike price is $32.• The continuously compounded risk-free rate is 5%.• The stock
A price of a nondividend-paying stock is currently $40.It is known that at the end of one month the stock’s price will be either $42 or $38.The risk-free interest rate is 8% per annum with
The current price of a nondividend-paying stock is S(0) = 100. The price of the stock at the end of one year, S(1), is either 90 or 120. The continuously compounded risk-free interest rate is
You use the following information to construct a binomial forward tree for modeling the price movements of a stock. (This tree is sometimes called a forward tree.)(i) The length of each period is one
For a one-year straddle on a nondividend-paying stock, you are given:(i) The straddle can only be exercised at the end of one year.(ii) The payoff of the straddle is the absolute value of the
The following one-period binomial stock price model was used to calculate the price of a one-year 10-strike call option on the stock.You are given:(i) The period is one year.(ii) The true probability
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 4 months.(ii) The current stock price is 41.(iii)
Suppose that the current stock price is $30 per share. At the end of 6 months, the stock price will be either $25 or $38. The 6-month effective risk-free interest rate is 10%.A European-type
For a two-period binomial model for stock prices, you are given:(i) Each period is 6 months.(ii) The current price for a nondividend-paying stock is $70.00.(iii) u = 1.181, where u is one plus the
For a two-period binomial stock price model, you are given:(i) The length of each period is 1 year.(ii) The (incomplete) price evolution of a 2-year European call option on the stock:Calculate the
Rework Example 4.1.3 using risk-neutral valuation.Data from Example 4.1.3For a one-year straddle on a nondividend-paying stock, you are given:(i) The straddle can only be exercised at the end of one
You are given:(i) The current price of a stock is $65.(ii) One year from now the stock will sell for either $60 or $70.(iii) The stock pays dividends continuously at a rate proportional to its price.
You are given the following information about American options on a stock:• The current stock price is 72.• The strike price of the options is 80.• The continuously compounded risk-free rate is
You are given the following regarding stock of Widget World Wide (WWW):(i) The stock is currently selling for $50.(ii) One year from now the stock will sell for either $40 or $55.(iii) The stock pays
For a one-period arbitrage-free binomial model with two nondividend-paying securities, you are given:(i) The following price evolution of the two securities:(ii) The following information about two
For a 10-period binomial stock price model, you are given:(i) The length of each period is one year.(ii) The current stock price is 1,000.(iii) At the end of every year, the stock price will either
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 one year.(ii) The current stock price is 82.(iii)
You are given the following information about a securities market:• There are two nondividend-paying stocks, X and Y .• The current prices for X and Y are both $100.• The continuously
You use the following information to construct a one-period binomial forward tree for modeling the price movements of a nondividend-paying stock. (The tree is sometimes called a forward tree.)(i) The
In an arbitrage-free securities market, there are two nondividend-paying stocks, A and B, both with current price $90. There are two possible outcomes for the prices of A and B one year from now:The
An arbitrage-free securities market model consists of a bank account and one security. The security price today is 100. The security price one year from now will be either 104 or 107.Determine which
You are to use a binomial forward tree model to model the price movements of a stock that pays dividends continuously at a rate proportional to its price. The length of each period is three months.
You are given the following with respect to a public company:• The common shares of the company were trading at 100 as of December 31, 2015.• No dividends are paid.• An industry analyst has
For a binomial option pricing model, you are given the following information:• The current stock price is $110.• The strike price is $100.• The interest rate is 5% (continuously compounded)•
A three-month European call is modeled by a single period binomial tree using the following parameters:• Continuously compounded risk-free rate = 4%• Dividend = 0• Annual volatility = 15%•
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 190.(iii)
A one-year European call option is currently valued at 0.9645. The following parameters are given.• Current stock price = 10• Continuously compounded risk-free rate = 6%• Continuously
For a 10-period binomial stock price model, you are given:(i) The length of each period is one year.(ii) The current stock price is 1,000.(iii) At the end of every year, the stock price will either
You are to estimate a nondividend-paying stock’s annualized volatility using its prices in the past nine months.Calculate the historical volatility for this stock over the period.(A) 83%(B) 77%(C)
Let S(t) be the time-t price of a nondividend-paying stock. For a three-period binomial stock price model, you are given:(i) The length of each period is one year.(ii) S(0) = 100.(iii) u = 1.1, where
For a two-period binomial model for stock prices, you are given:(i) The length of each period is one year.(ii) The current price of a nondividend-paying stock is $150.(iii) u = 1.25, where u is one
For a two-period binomial model for stock prices, you are given:(i) The length of each period is one year.(ii) The current price of a nondividend-paying stock is $40.(iii) u = 1.05, where u is one
For a binomial forward tree modeling the price movements of a stock, you are given:(i) The length of each period is 6 months.(ii) The current price of a nondividend-paying stock is $9,000.(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 4 months.(ii) The current stock price is 100.(iii)
The Ashwaubenon Company (Ash Co) needs to raise capital to support its rapidly growing business. One proposal is to publicly issue a certain number of equity units, each of which consists of one
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 4 months.(ii) The current stock price is 55.(iii)
You use the following information to construct a two-period binomial forward tree for modeling the movements of the dollar-euro exchange rate:(i) The current dollar-euro exchange rate is
For a four-period binomial tree model for the dollar/pound exchange rate, you are given:(i) The length of each period is 3 months.(ii) The current dollar/pound exchange rate is 1.4.(iii) u = 1.1 and
You use the following information to construct a binomial tree for modeling the price movements of a futures contract on the S&V 150:(i) The length of each period is 6 months.(ii) The initial futures
You use the following information to construct a one-period binomial forward tree for modeling the price movements of a nondividend-paying stock:(i) The current stock price is 82.(ii) The stock’s
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 4 months.(ii) The current stock
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 4 months.(ii) The current stock
Assume the Black-Scholes framework. Let S(t) denote the time-t price of a nondividend-paying stock. You are given: (i) The current stock price is 38. (ii) The stock’s volatility is 35%. (iii)
You are given the following information about a European call option. • The current stock price is $35.• The exercise price is $40.• The option matures in 6 months.• The expected return on
Consider a nondividend-paying stock whose current price is 100.The stock-price process is a lognormal process with volatility 30%.The continuously compounded expected return on the stock is 10%.The
You are given the following information about a nondividend-paying stock:(i) The current stock price is 100.(ii) Stock prices are lognormally distributed.(iii) The continuously compounded expected
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 2.5%.(iii)
Assume the Black-Scholes framework.You are given the following information for a stock that pays dividends continuously at a rate proportional to its price.(i) The current stock price is 0.25.(ii)
Two actuaries, A and B, use a two-period binomial forward tree to compute the prices of a European call and a European put using different parameters.You are given:Describe the relationship between

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