Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Question
Chapter 20, Problem 22PS
Summary Introduction
To calculate: A zero-net-investment arbitrage strategy for exploitation of pricing anomaly and draw a profit diagram at expiry.
Introduction:
Zero net investment arbitrage strategy: When the securities are purchased and sold in such a way that it makes the net investment value as 0, this sort of strategy is known as zero net investment arbitrage strategy. When this strategy is used, both buying and selling of securities are done together to avail the benefit.
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Select all that are true with respect to the Black Scholes Option Pricing Model (OPM) in practice):
Group of answer choices
BSOPM assumes that the volatility of the underlying stock returns is constant over time.
BSOPM assumes that the underlying stock can be traded continuously.
BSOPM assumes that there are no transaction costs.
There is only one input to the BSOPM that is not observable at the time you are valuing a stock option, and that input is volatility.
Implied volatility is estimated by calculating the daily volatility of the underlying stock’s return that occurred over the prior six months.
Consider the following options, which have the same two-year maturity and are written on the same
stock. The firm does not pay dividends.
Put option P1 has a strike price Xp1 = $50
Put option P2 has a strike price Xp2 = $100
Call option C1 has a strike price Xc1 = $100
Call option C2 has strike price Xc2 = $50
Your broker offers two trading strategies that can be derived from the options above.
Strategy A: Long two puts P1 and long two calls C1
Strategy B: Long two calls C2 and long two puts P2
A. Which strategy would you choose if the two strategies have the same costs? Explain your
answer.
You now collect more information about the available securities. The stock has an implied volatility of
45% p.a.. The current risk-free rate is 1% p.a. The current stock price is $56.
B. Calculate the value of the call option C1 using the Black-Scholes formula. Explain why such a
deep out-of-the-money option still has a positive valuere:
C. Calculate the cost of strategy B using the Black-Scholes…
The hedge ratio of an at-the-money call option on IBM is 0.36. The hedge ratio of an at-the-money put option is -0.64. What is the
hedge ratio of an at-the-money straddle position on IBM? (Negative answer should be indicated by a minus sign. Round your answe
to 2 decimal places.)
Hedge ratio
Chapter 20 Solutions
Investments
Ch. 20 - Prob. 1PSCh. 20 - Prob. 2PSCh. 20 - Prob. 3PSCh. 20 - Prob. 4PSCh. 20 - Prob. 5PSCh. 20 - Prob. 6PSCh. 20 - Prob. 7PSCh. 20 - Prob. 8PSCh. 20 - Prob. 9PSCh. 20 - Prob. 10PS
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- II. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5 a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model? c. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question (a) and (b) above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?arrow_forwardWhich of the following is true: The BSM model combined with the put call parity can be used to give the theoretical price of an American put option. One of the variables that influences the price of the option is the expected return on the stock. Since dividends could trigger an early exercise of an American call, the BSM formula dividend adjustment will provide the correct price of an American call. The BSM formula requires cumulative probabilities from the lognormal distribution. The BSM model may be used with currency options by replacing the dividend yield with the foreign interest rate.arrow_forwardTick all those statements on options that are correct (and don't tick those statements that are incorrect). B a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. b. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ker where T is the expiry time. An American put option should never be exercised before the expiry time. d. In general the equation S(T) +(K-S(T)) = (S(T)-K)+ +K is valid. e. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. C.arrow_forward
- At time t = 0, a trader takes a long position in a futures contract on stock i that willexpire at time T. the present value of this contract to the long is given by: See Image.Assume no-arbitrage pricing. Show analytically that if the return from stock i is positively correlated with the overall return on the stock market, then the futures market must be in backwardation at time t = 0.arrow_forward1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.arrow_forwardCan you please help with the question in the picture attached? The answer should be only one and I’m quite confused. Thank you!arrow_forward
- Consider the following information: Put Premium: $0.46 Strike Price: $32.82 Price of the underlying at initiation: $35.00 Calculate the breakeven price on a protective put option strategy (The breakeven price is the price of the underlying that would lead to a profit of $0).arrow_forwardWhat insights does the Black-Scholes option pricing model provide about financial derivatives? The Black-Scholes model is a mathematical model used to determine the fair price or theoretical value of a European-style option. It incorporates variables such as the current stock price, option strike price, time until expiration, risk-free rate, and stock volatility. The model assumes that stock prices follow a log-normal distribution and that markets are efficient, with no transaction costs or taxes. While originally developed for stock options, its principles have been extended to value various types of financial derivatives. The Black-Scholes model revolutionized the field of quantitative finance and played a crucial role in the growth of the derivatives market. Despite its limitations and assumptions, it remains a fundamental tool in options trading and risk management.arrow_forwardplease give me answerarrow_forward
- 2. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model. 3Suppose a European put options has a price higher than that dictated by the putcall parity.a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question 2 above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?arrow_forwardConsider the following quoted spot rates and identify which statement(s) below is(are) true: Spot Bid Rate Spot Ask Rate AUD1.5455/USD AUD1.5656/USD USD1.2599/GBP USD1.2685/GBP AUD1.9547/GBP AUD1.9638/GBP O a. A riskless arbitrage can be made only by going "clockwise" around the triangle. O b. None of the options in this question is true. O c. A riskless arbitrage can be made only by going "anti-clockwise" around the triangle.arrow_forwardSelect all that are true with respect to the Black Scholes Option Pricing Model (BSOPM) Group of answer choices When using BSOPM to value a stock option, the BSOPM assumes that stock prices follow a normal distribution. When using BSOPM to value a stock option, the BSOPM assumes that stock returns follow a normal distribution. Half of the observations in a normal distribution are above the mean and half are below the mean. Fisher Black and Myron Scholes were awarded the Nobel Prize in 1997 for their work in Option Pricing.arrow_forward
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