Question Assume the Black-Scholes framework. Consider a call option on a non- dividend paying stock. You are given: i) The strike price is 110% of the stock price ii) N (d₁) = 0.31075 iii) N (d₂) = 0.25987 Determine the elasticity of the call option. Possible Answers A 8.8 B 9.4 C 10.0 D 10.6 E 11.2

Question Assume the Black-Scholes framework. Consider a call option on a non- dividend paying stock. You are given: i) The strike price is 110% of the stock price ii) N (d₁) = 0.31075 iii) N (d₂) = 0.25987 Determine the elasticity of the call option. Possible Answers A 8.8 B 9.4 C 10.0 D 10.6 E 11.2

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Use the Black-Scholes formula to find the value of a call option based on the following inputs. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value $ 51 $ 64 0.068 0.04 0.50 0.265
Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26
Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option X
1. 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.
Consider two European call options with strike K and the same underlying non- dividend paying stock. The stock price is currently at So. Option 1 has price C₁ maturity T₁ and Option 2 has price C₂ and maturity T2, where T₂ > T₁. The risk-free interest rate is r. Use a no-arbitrage argument to prove that C₂ > C₁-
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 Profit
1. An option is trading at $5.26, has a delta of .52, and a gamma of .11. what would the delta of the option be if the underlying increases by $.75? What would the delta of the option be if the underlying decreases by $1.05? Explain.
QUESTION 2. Consider a stock valued So at time t = 0, and taking only two possible values S1 = S, or Si = S1 at time t = 1, with S, < I1. a) Compute the initial portfolio allocation (a, 3) of a portfolio made of a units of stock and $B in cash, hedging the call option with strike price K e [S,,3¡] and claim payoff Si – K if Si = 3ı C = (Si – K)* $0 if S = S1, at time t = 1. b) Show that the risky asset allocation a satisfies the condition a € [0, 1]. c) Compute the Superhedging Risk Measure SRMc' of the claim C = (S1 – K)+.
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.
D3) 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.
Use the put-call parity relationship to demonstrate that an at-the-money call option on a nondividend-paying stock must cost more than an at-the-money put option. Show that the prices of the put and call will be equal if S0 = (1 + r)T..
Problem 4d: State whether the following statements are true or false. In each case, provide a brief explanation. d. In a binomial world, if a stock is more likely to go up in price than to go down, an increase in volatility would increase the price of a call option and reduce the price of a put option. Note that a static position is a position that is chosen initially and not rebalanced through time.

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