Questions and Answers of Derivative Pricing

Assume the Black-Scholes framework. For a European put option and a European gap call option on a stock, you are given:(i) The expiry date for both options is T.(ii) The put option has a strike price
You are given the following:• The current price to buy one share of XYZ stock is 500.• The stock does not pay dividends.• The annual risk-free interest rate, compounded continuously, is 6%.•
You are given:(i) The following 1-year European put option prices on the same stock:(ii) The continuously compounded risk-free interest rate is 6%. You take advantage of any possible mispricing by
Explain intuitively when you will expect that CE ≈ FP0,T(S).
Consider European and American options on a nondividend-paying stock.You are given:(i) All options have the same strike price of 100.(ii) All options expire in six months.(iii) The continuously
On April 30, 2007, a common stock is priced at $52.00. You are given the following:(i) Dividends of equal amounts will be paid on June 30, 2007 and September 30, 2007.(ii) A European call option on
You are given:• C(K, T) denotes the current price of a K-strike T-year European call option on a nondividend-paying stock.• P(K, T) denotes the current price of a K-strike T-year European put
For a stock, you are given:(i) The current stock price is $50.00.(ii) δ = 0.08.(iii) The continuously compounded risk-free interest rate is r = 0.04.(iv) The prices for one-year European calls (C)
You are given:(i) The following prices of 3-year European call options on the same stock:(ii) The continuously compounded risk-free interest rate is 2%. To earn arbitrage profit, you buy two
A nine-month dollar-denominated call option on euros with a strikeprice of $1.30 is valued at $0.06. A nine-month dollar-denominated put option on euroswith the same strike price is valued at 0.18.
Near market closing time on a given day, you lose access to stock prices, but some European call and put prices for a stock are available as follows:All six options have the same expiration
You are given:(i) The current exchange rate is 0.011$/¥.(ii) A four-year dollar-denominated European put option on yen with a strike price of $0.008 sells for $0.0005.(iii) The continuously
Given the following chart about call options on a particular dividend-paying stock, which option has the highest value?(A) Option A(B) Option B(C) Option C(D) Option D(E) Option E
You are given the following information on a stock:Assume that the log returns are normally distributed. (a) Calculate the 95% prediction interval for the stock price in one year. (b) Calculate the
Assume the Black-Scholes framework. You are given:(i) The stock, whose current price is 100, pays dividends continuously at a rate proportional to its price.(ii) The stock’s volatility is
Assume the BlackScholes framework. Let S(t) denote the time-t price of a stock, which pays dividends continuously at a rate proportional to its price.You are given:(i) S(0) = 8 (ii) The 90%
Assume the Black-Scholes framework. Determine an expression for E[S(T)|a < S(T) < b], where a and b are positive constants with a < b.
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:(i) The stock pays dividends continuously at a rate proportional to its price.(ii) The 90%
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 2-year at-the-money European put option
Assume the Black-Scholes framework. You are given:(i) The current price of a stock is 80.(ii) The stock’s volatility is 25%.(iii) The stock pays dividends continuously at a rate proportional to its
Assume the Black-Scholes framework. You are given:(i) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is identical to the continuously compounded (total)
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 an 8-month European put option on the
Which of the following is an assumption of the Black-Scholes option pricing model?(A) Stock prices are normally distributed.(B) Stock price volatility is a constant.(C) Changes in stock price are
For a six-month European put option on a stock, you are given:(i) The strike price is $50.00.(ii) The current stock price is $50.00.(iii) The only dividend during this time period is $1.50 to be paid
Your company has just written a one-year European putoption on an equity index fund.The equity index fund is currently trading at 1000. It pays dividends continuously at arate proportional to its
Assume the Black-Scholes framework. You are given:(i) The stock price is 100.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.(iii) The
You are considering the purchase of 100 units of a 3-month 25-strike European call option on stock.You are given:(i) The Black-Scholes framework holds.(ii) The stock is currently selling for 20.(iii)
You are considering the purchase of a three-month 41.5-strike American call option on a nondividend-paying stock.You are given:(i) The Black-Scholes framework holds.(ii) The stock is currently
Consider a one-year 45-strike European put option on a stock S. You are given:(i) The current stock price, S(0), is 50.00.(ii) The only dividend is 5.00 to be paid in nine months.(iii) Var[ln
Assume the Black-Scholes framework. For an at-the-money, 8-month European put option on a stock, you are given:(i) The stock pays dividends continuously at a rate proportional to its price. The
On January 1st, 2007, the following currency information is given:• Spot exchange rate = $0.82/euro• Dollar interest rate = 5.0% compounded continuously• Euro interest rate = 2.5% compounded
You are asked to determine the price of a European put option on a stock.Assuming the Black-Scholes framework holds, you are given:(i) The stock price is $100.(ii) The put option will expire in 6
Assume the Black-Scholes framework. Consider a 3-year European contingent claim on a stock. For t ≥ 0, let S(t) be the time-t price of the stock.You are given:(i) S(0) = 45.(ii) The stock’s
Assume the Black-Scholes framework. You are given:(i) The stock price is 100.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.(iii) The
Company A is a US international company, and Company B is a Japanese local company. Company A is negotiating with Company B to sell its operation in Tokyo to Company B. The deal will be settled in
Assume the Black-Scholes framework. You are given:(i) The current price of a stock is 80.(ii) The stock’s volatility is 25%.(iii) The stock pays dividends continuously at a rate proportional to its
Which of the following otherwise identical European options has the highest gamma?(A) 1-day deep out-of-the-money call option(B) 10-day deep in-the-money call option(C) 1-year at-the-money put
Assume the Black-Scholes framework. Consider a 9-month at-the-money European put option on a futures contract. You are given:(i) The continuously compounded risk-free interest rate is 10%.(ii) The
Consider a stock with current price $50. You are given:(i) There will be only one dividend; $2 will be paid in three months.(ii) σ = 0.30.(iii) The continuously compounded risk-free interest rate is
You compute the current delta for a 50-60 bull spread with the following information:(i) The continuously compounded risk-free rate is 5%.(ii) The underlying stock pays no dividends.(iii) The current
A call option is modeled using the Black-Scholes formula with the following parameters.• S = 25• K = 24• r = 4%• δ = 0%• σ = 20%• T = 1Calculate the call option elasticity, Ω.(A) Less
Assume the Black-Scholes framework. For a 9-month 45-55 put bear spread on a stock, you are given:(i) The current stock price is 50.(ii) The only dividends during this time period are 2.50 to be paid
Assume the Black-Scholes framework. Consider a 1-year European contingent claim on a stock. You are given:(i) The time-0 stock price is 45.(ii) The stock’s volatility is 25%.(iii) The stock pays
Assume the Black-Scholesframework. You are given:(i) The current stock price is $82.(ii) The stock’s volatility is 30%.(iii) The stock pays no dividends.(iv) The continuously compounded risk-free
Assume the Black-Scholes framework. Consider a stock, and a European call option and a European put option on the stock. The current stock price, call price, and put price are 45.00, 4.45, and 1.90,
Assume the Black-Scholes framework. For a 3-month at-the-money European put option on a stock, you are given:(i) The stock is currently selling for 50.(ii) The stock will pay a single dividend of 1.5
You are given the following information about 50-strike and 60-strike European put options with the same stock and time to expiration:Calculate the elasticity of a 50-60 European put bull spread.
Assume the Black-Scholes framework. Consider a 3-month European contingent claim on a stock.You are given:(i) The stock is currently selling for 50.(ii) The stock will pay a single dividend of 1.5 in
You are given:(i) The current dollar-euro exchange rate is 1.50$/AC.(ii) The volatility of the exchange rate is 20%.(iii) The continuously compounded risk-free interest rate on dollars is 3%.(iv) The
You have ordered a Rolls Royce car for the price of 200,000 British pounds, which you will pay when the car is delivered to you in three months. The current exchange rate is 1.60 US dollars per
To settle an urgent debt of US $300,000 payable in three months, you have decided to (reluctantly!) sell your favorite Rolls Royce car for the price of 200,000 British pounds, which you will receive
Assume the Black-Scholes framework. You are given:(i) The current dollar/euro exchange rate is 1.50$/€.(ii) The volatility of the exchange rate is 20%.(iii) The continuously compounded risk-free
Assume the Black-Scholes framework.You are given:(i) The current price of the P&K 777 index is 500.(ii) The P&K 777 index pays dividends continuously at a rate proportional to its price. The
Assume the Black-Scholes framework.Consider a 95-strike 9-month European call option on an S&V 150 futures contract which matures one year from now. You are given:(i) The current price of the S&V 150
Assume the Black-Scholes framework. Which of the following graphs best represents the relationship between the delta of a deep out-of-the-money European call option on a nondividend-paying stock and
Assume the Black-Scholes framework.Consider a 6-month 90-strike European put option on a futures contract. You are given:(i) The price of the underlying futures contract is 95.(ii) The delta of the
Assume the Black-Scholes framework. Consider European call and put options on a stock that pays dividends continuously at a rateproportional to its price.Determine the signs of the following twelve
Determine the limiting value of gamma as we approach maturity (i.e., find limT→0Γ) for each of the following options:(a) A deep in-the-money European call option(b) A deep out-of-the-money
(a) If the strike price of a European call option decreases, then how will the price of the call change, holding everything else constant?(b) Verify your conclusion in part (a) by general
Assume the Black-Scholes framework. Consider a long K-strike European straddle. For each of delta and gamma, discuss intuitively how the option Greek of the straddle varies with S, the current stock
Youcompute the current gamma for a 50-60 bull spread with the following information:(i) The continuously compounded risk-free interest rate is 5%.(ii) The underlying stock pays no dividends.(iii) The
Assume the Black-Scholes framework. You are given:(i) The current dollar/euro exchange rate is 1.2.(ii) The continuously compounded risk-free interest rate in the United States is 2%.(iii) The
Assume the Black-Scholes framework. You are given:(i) The current stock price is 82.(ii) The stock’s volatility is 30%.(iii) The stock pays dividends continuously at a rate proportional to its
Assume the Black-Scholes framework.Consider a one-year at-the-money European put option on a nondividend-paying stock.You are given:(i) The ratio of the current put option price to the current stock
Assume the Black-Scholes framework. Consider a portfolio consisting of three European options, X, Y, and Z, on the same stock. You are given:Calculate the elasticity of the portfolio. Option
Assume the Black-Scholes framework. For a 3-month 32-strike European straddle on a stock, you are given:(i) The stock currently sells for $30.(ii) The stock’s volatility is 30%.(iii) The stock pays
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock.Consider a 9-month European contingent claim on the stock. You are given:(i) The stock’s volatility is
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a nondividend-paying stock. You are given:(i) S(0) = 100.(ii) Var[ln S(t)] = 0.16t, for t ≥ 0.(iii) The continuously
For two European call options, Call-I and Call-II, on a stock, you are given:Suppose you just sold 1000 units of Call-I. Determine the numbers of units of Call-II and stock you should buy or sell in
Your company has just sold a European put option on 10,000 USD for a premium paid in Japanese yen.You are given the following:• The time to maturity T = 180 days • Yen risk-free interest rate rj
Assume the Black-Scholes framework. Four months ago, Eric bought 100 units of a one-year 45-strike European call option on a nondividend-paying stock. He immediately delta-hedged his position with
Assume that the Black-Scholes framework holds. The price of a nondividend-paying stock is $30.00. The price of a put option on this stock is $4.00.You are given:(i) ∆ = −0.28(ii) Γ = 0.10 Using
Several months ago, an investor sold 100 units of a one-year European call option on a nondividend-paying stock. She immediately delta-hedged the commitment with shares of the stock, but has not ever
An investor has a portfolio consisting of 100 put options on stock A, with a strike price of 40, and 5 shares of stock A. The investor can write put options on stock A with a strike price of 35. The
One year ago, Jacky bought 10 units of a 2-year at-the-money European straddle on a nondividend-paying stock. He immediately delta-hedged his position with shares of the stock, but has not ever
Assume that the Black-Scholes framework holds. Consider an option on a stock.You are given the following information at time 0:(i) The stock price is S(0), which is greater than 80.(ii) The option
You hold a trading book consisting of many long/short positions in Tempranillo Corp. stock and options. You are analyzing two possible scenarios for Tempranillo Corp. stock and want to make money by
Assume the Black-Scholes framework.One month ago, Tidy bought 1,000 units of a 9-month 60-strike European put option on a stock. He immediately delta-hedged the commitment with shares of the stock,
Assume you have purchased European put options for 100,000 shares of a nondividend-paying stock and you are given the following information.• Price of stock = $49.16• Strike price = $50.00•
Assume the Black-Scholes framework. You are given:(i) The current price of a nondividend-paying stock is 80.(ii) An investor has sold 1,000 units of a one-year at-the-money European call option on
Consider the Black-Scholes framework. A market-maker, who delta-hedges, sells a three-month at-the-money European call option on a nondividend-paying stock.You are given:(i) The continuously
Assume the Black-Scholes framework. You are given:(i) The current stock price is 50.(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.(iii) The
Assume the Black-Scholes framework. You are given:(i) The current price of a nondividend-paying stock is 20.(ii) The stock’s volatility is 28%.(iii) The continuously compounded risk-free interest
Assume the Black-Scholes framework.Eight months ago, an investor borrowed money at the risk-free interest rate to purchase a one-year 75-strike European call option on a nondividend-paying stock. At
Assume the Black-Scholes framework. Consider a derivative security of a stock.You are given:(i) The continuously compounded risk-free interest rate is 0.04.(ii) The volatility of the stock is
A market-maker has sold 100 call options, each covering 100 shares of a dividend-paying stock, and has delta-hedged by purchasing the underlying stock.You are given the following information about
Assume the Black-Scholes framework. Yesterday, you sold a European call option on a nondividendpaying stock. You immediately delta-hedged the commitment with shares of the stock.Today, you decide to
For two European call options, Call-I and Call-II, on a stock, you are given: Suppose you just sold 1,000 units of Call-I. You buy or sell appropriate units of the stock and Call-II in order to both
Assume the Black-Scholes framework. You are given: (i) The current price of a stock is 60. (ii) The stock pays no dividends. (iii) The stock’s volatility is 30%. (iv) The continuously
Assume the Black-Scholes framework. You are given:(i) The current price of a nondividend-paying stock is 50.(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 price of a stock is $50.(ii) The stock pays no dividends.(iii) The stock’s volatility is 25%.(iv) The continuously compounded
Assume the Black-Scholes framework. The current prices of a stock and a call option on the stock are $10 and $2, respectively.You are given:(i) ∆ = 0.6(ii) Γ = 0.2Use the delta-gamma approximation
Assume the Black-Scholes framework. For a 3-month 80-strike European put option on a nondividend-paying stock, you are given:(i) The current price of the stock is 75.(ii) The current price of the put
Assume the Black-Scholes framework. Consider a 9-month at-the-money European put option on a futures contract.The continuously compounded risk-free interest rate is 8%.The futures price
Assume the Black-Scholes framework. You are given:(i) The current price of a nondividend-paying stock is 70.(ii) The stock’s volatility is 25%.(iii) The continuously compounded risk-free interest
Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a nondividend-paying stock and V (s, t) be the time-t price of a European derivative when the price of the underlying
Assume the Black-Scholes framework. Determine all value(s) of a, in terms of r, σ, γ, such that V (S(t), t) := AS(t)aeγt represents the time-t price of a derivative security on a
Assume the Black-Scholes framework. One year ago, Kelvin bought 1,000 units of a European call option on a nondividend-paying stock. He immediately delta-hedged his position with appropriate number
Assume the Black-Scholes framework. Three months ago, Tyler bought 100 units of an at-the-money European call option on a nondividend-paying stock.He immediately delta-hedged his position with
Assume the Black-Scholes framework. Three months ago, you sold 1,000 units of a 1-year European put option on a nondividend-paying stock. You immediately delta-hedged your position with appropriate

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