INVESTMENTS(LL)W/CONNECT
11th Edition
ISBN: 9781260433920
Author: Bodie
Publisher: McGraw-Hill Publishing Co.
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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.
As an option trader, you are constantly looking for opportunities to make an arbitrage transaction (that is, a trade in which you do not need to commit your own capital or take any risk but can still make a profit). Suppose you observe the following prices for options on DRKC Co. stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six-month T-bill is $97.00 (for face value of $100).
a. Using the put-call-spot parity condition, demonstrate graphically how you could synthetically re-create the payoff structure of a share of DRKC stock in six months, using a combination of puts, calls, and T-bills transacted today.
b. Given the current market prices for the two options and the T-bill, calculate the no-arbitrage price of a share of DRKC stock.
c. If the actual market price of DRKC stock is $60, demonstrate the arbitrage transaction you could create to…
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…
Chapter 20 Solutions
INVESTMENTS(LL)W/CONNECT
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- Label the following for this diagram: a. Name of options payoff b. Identify whether positive or negative premium c. Identify breakeven point d. What is the profit or loss when stock price is S60 at maturity e. Suppose you have this options position, should you exercise your right (if any) assuming that the stock price is $60 at maturity? Option Payoffs and Profits Long put $40 $20 $0 Option Payoff Option Profit Exerche Price $20 S40 $20 $40 S60 $80. Stock Price At Maturity Payoff and Profitarrow_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
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