In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be
a.
Put | T | X | 0 | Price of Put |
A |
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B |
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Which put option is written on the stock with the lower price?
(1) A
(2) B
(3) Not enough information
b.
Put | T | X | 0 | Price of Put |
A |
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B |
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Which put option must be written on the stock with the lower price?
(1) A
(2) B
(3) Not enough information
c.
Put | T | X | 0 | Price of Put |
A |
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B |
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Which call option must have the lower time to expiration?
(1) A
(2) B
(3) Not enough information
d.
Call | T | X | 0 | Price of Call |
A |
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B |
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Which call option is written on the stock with higher volatility?
(1) A
(2) B
(3) Not enough information
e.
Call | T | X | 0 | Price of Call |
A |
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B |
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Which call option is written on the stock with higher volatility?
(1) A
(2) B
(3) Net enough information
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- A call option with X = $55 on a stock priced at S = $60 is sells for $12. Using a volatility estimate of σ = 0.35, you find that N(d1) = 0.7163 and N(d2) = 0.6543. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than 0.35?arrow_forwardA call option with X = $50 on a stock currently priced at S = $55 is selling for $10. Using a volatility estimate of σ = .30, you find that N(d1 ) = .6 and N(d2 ) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.arrow_forwardAn option is trading at $3.45. If it has a delta of .78, what would the price of the option be if the underlying increases by $.75? A. What would the price of the option be if the underlying decreases by $.55? B. What makes this a call option? C. With a delta of .78, is this option ITM, ATM or OTM and how?arrow_forward
- 2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.arrow_forward4. Consider an exchange option. Suppose the initial prices (time 0) of the two stocks are S =S2 = 100 and a =0.40,. Suppose also that the returns on the stocks are uncorrelated. Assume no dividends and final maturity of the option is T = 2 year: (a) Using the closed-form expressions for the price of these options, identify the price of the exchange option when o = 0, a2 =0.20, ag =0.40, and @2 =0.60. (b) Is there a trend in the price? Intuitively, why is this the case?arrow_forwardD3) Finance Consider an option with α being a non-negative parameter and the option pays ((S(T))α − K)+ at maturity date T. Let Cα(S(0), σ, r) be the risk neutral price of the option (with interest rate r and volatility σ) when the initial price is S(0). Obviously, C1(S(0), σ, r) = C(S(0), σ, r) is the price of an ordinary call option. Show that, Cα(S(0), σ, r) = e(α−1)(r+ασ2/2)TC((S(0))α, ασ, rα), where rα = α(r − σ2/2) + α2σ2/2.arrow_forward
- V3. By looking at the sensivities of your portfolio to δs = -$2 and δσ = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.)arrow_forwardConsider two put options on the same stock with the same time to maturity. The strike price of Put A is less than the strike price of Put B. Which of the following is true? O It is possible for Put A to be in the money and Put B to be out of the money. O It is possible for Put A to be out of the money and Put B to be in the money. One of the options must be in the money. All of the other answers are correct.arrow_forwardConsider a call option whose maturity date is T and strike price is K. At any time t < T, is it always the case that the call option's price must be greater than or equal to max(St – K,0), where St is the stock price at t? (Your answer cannot be more than 30 words. Answers with more than 30 words will not be graded.)arrow_forward
- 4. Consider a stock with a current price of S0 = $60. The value of the stock at time t = 1 can take one of two values: S1,u = $100, S1,d = $40. The price of a risk-free bond that pays out $1 in period t = 1 is $0.90. (a) Using a one-step binomial tree, write down the possible payoffs of a put option on stock S with strike K = $60 and maturity t = 1. (b) What is the price of this put option? (c) What is the price of a call option with strike K = $60 and maturity t = 1? Please use put-call parity to find the call price.arrow_forwardK1.arrow_forwardYou write a put option with X = 100 and buy a put with X = 110. The puts are on the same stock and have the same expiration date.a. Draw the payoff graph for this strategy.b. Draw the profit graph for this strategy.c. If the underlying stock has positive beta, does this portfolio have positive or negative beta?arrow_forward
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