Please correct answer and don't used hand raiting Question 3Consider a European call option and a European put option that have the same under-lying stock, the same strike price K, and the same expiration date T. Let C denote the Callpremium, P denote the Put premium, and S denote the current stock price. Suppose therisk-free borrowing rate r is greater than the risk-free lending rate rɩ, i.e., rɩ > ri.Suppose C < P+S - Ke¯T. Are there arbitrage opportunities? If so, describe yourtrading strategy; otherwise, list a condition involving r₁, under which an arbitrage strategyexists and describe the strategy.

Arbitrage OpportunityYes, an arbitrage opportunity exists if this inequality holds. Here's…

Answered: Question 3 Consider a European call…

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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Question 1. Suppose t ≤ T1 ≤ T2 ≤ T3, where t is the current time, and ∆ > 0. Recall that Z(T1, T2) is the price at time T1 of a ZCB with maturity T2 and F(T1, T2, T3) is the forward price at time T1 for a forward contract with maturity T2 on a ZCB with maturity T3. a) For each of the pairs of A and B in the table, choose the most appropriate relationship out of ≥, ≤, = , ?, where ? means the relationship is indeterminate. Give brief reasoning. A ≥, ≤, = , ? B (i) Z(t, T1) 1 (ii) Z(T1, T1) 1 (iii) Z(t, T2) Z(t, T3) (iv) Z(T1, T2) Z(T1, T3) (v) Z(T1, T3) Z(T2, T3) (vi) Z(T1, T1 + ∆) Z(T2, T2 + ∆) (vii) F(t, T1, T2) F(t, T1, T3) (viii) F(t, T1, T3) F(t, T2, T3) (ix) limT→∞ Z(t, T) 0 Hint: Remember that at current time t, F(t, ·, ·) is known but Z(T, ·) is a random variable. b) What can you say about interest rates between T1 and T2 if i) Z(t, T1) = Z(t, T2)? ii) Z(t, T1) > 0 and Z(t, T2) = 0?
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.
Tick 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.
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.
Let C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?
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Tick all those statements on options that are correct (and don't tick those statements that are incorrect). O a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. Ob. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. 0 C. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ke where I is the expiry time. Od. In general the equation S(T) + (K − S(T))+ (S(T) — K)† + K is valid. An American put option should never be exercised before the expiry time. e. =
Consider a two-factor Arbitrage Pricing Theory (APT) model, T; = a; + b1,ifı + b2.i f2 + €i, with the following information Asset i Asset 1 0.07 0.50 0.25 Asset 2 0.15 1.10 0.75 Asset 3 0.20 b1,3 Hi b1i b2i 1.0 and the risk-free rate rp is 0.025. (a) Find the value of b13 to preclude arbitrage opportunity. (b) is an Asset 4 with 4 = 0.13, b14 = 0.8, and b2.4 = 0.4. Explain how you would exploit an arbitrage opportunity if there

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