Essentials Of Investments
11th Edition
ISBN: 9781260316193
Author: Bodie
Publisher: MCG
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Textbook Question
Chapter 16, Problem 9PS
a. Calculate the value of a call option on the stock in the previous problem with an exercise price of
b. Verify that the put-call parity relationship is satisfied by your answers to both Problems
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4. Valuation of a Derivative
Consider a derivative on a stock with the time to expiration T and the following payoff:
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if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price
using N(), the cumulative probability distribution function of a standard normal random variable.
IT IS NOT DELTA
Option _______ is a percentage change in the value of the option per 1% change in the value of the underlying security.
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Chapter 16 Solutions
Essentials Of Investments
Ch. 16 - Prob. 1PSCh. 16 - A put option on a stock with a current price of 33...Ch. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - In each of the following questions, you are asked...Ch. 16 - Reconsider the determination of the hedge ratio in...Ch. 16 - Show that Black-Scholes call option hedge ratios...Ch. 16 - We will derive a two-State put option value in...Ch. 16 - a. Calculate the value of a call option on the...Ch. 16 - Prob. 10PS
Ch. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - Prob. 16PSCh. 16 - 17. Find the Black-Scholes value of a put option...Ch. 16 - Prob. 18PSCh. 16 - What would be the Excel formula in Spreadsheet...Ch. 16 - Prob. 20PSCh. 16 - Prob. 21PSCh. 16 - Prob. 22PSCh. 16 - Prob. 23PSCh. 16 - Prob. 24PSCh. 16 - Prob. 25PSCh. 16 - Prob. 26PSCh. 16 - Prob. 27PSCh. 16 - Prob. 28PSCh. 16 - Prob. 29PSCh. 16 - Prob. 30PSCh. 16 - Prob. 31PSCh. 16 - Prob. 32PSCh. 16 - Prob. 33PSCh. 16 - Prob. 34PSCh. 16 - Prob. 35PSCh. 16 - Prob. 36PSCh. 16 - Prob. 38CCh. 16 - Prob. 39CCh. 16 - Prob. 40CCh. 16 - Prob. 41CCh. 16 - Prob. 42CCh. 16 - Prob. 43CCh. 16 - Prob. 44CCh. 16 - Prob. 2CP
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- The correct formula to calculate the future value (FV) of a present value (PV) when simple interest is used is? Note: N would be number of periods and i would be the interest rate. A. FV = PV X (1+i)^N, where^ represents power B. FV = PV X (1+i)^-N, where^ represents power O C. FV = PV/((1+i) X N) D. FV = PV x (1 + (N x i)) Reset Selection Mark for Review What's This? The correct formula to calculate the future value (FV) of a present value (PV) when simple interest is used is? Note: N would be number of periods and i would be the interest rate. A. FV = PV X (1+i)^N, where^ represents power OB. FV = PV X (1+i)^-N, where^ represents power C. FV = PV /((1+i) x N) D. FV = PV x (1 + (N X i)) Reset Selection Mark for Review What's This?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_forwardQuestion 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?arrow_forward
- Consider a forward contract on a stock that pays dividends at specific times ti, where 0 < t1 < t2 < ... < tn < T. Suppose that the dividend is a fixed amount: Di at fixed times ti. Show that in this case, the forward contract price is given byarrow_forwardPlease asaparrow_forward6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)arrow_forward
- 2-2 What are the variaables in the BSM call option valuation model below and how do they affect call option pricing?arrow_forwardAssume that security returns are generated by the single-index model, Ri a BiRM + ei where R₁ is the excess return for security /and Ry is the market's excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security Bi E(Ri} #{@į) A 1.5 61 298 B 1.7 8 15 C 1.9 10 24 a. If oy 26%, calculate the variance of returns of securities A, B, and C. Answer is complete but not entirely correct. Variance Security A 1,521 Security B 1,609 Security C 2,440 b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)arrow_forwardSuppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price? Solutions:arrow_forward
- 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. =arrow_forwardConsider the following two scenarios whereby the cost-of-carry model is violated. You are required to select appropriate missing words and fill in question 1. a. long b. spot c. over priced d. short arbitrage e. under priced f. long arbitrage g. futures h. short Question 1 a. If ft >S0 (1 + rf - d)^t, then the( ) is ( )relative to ( ) or equivalently, the quoted futures price is higher than what it should be. Thus, the correct arbitrage strategy should be: ( ) the futures contract and ( )the spot market. This strategy is also known as ( ). b. If ft <S0 (1 + rf - d)^t, then the( ) is ( )relative to ( ) or equivalently, the quoted futures price is lower than what it should be. Thus, the correct arbitrage strategy should be: ( ) the futures contract and ( )the spot market. This strategy is also known as ( ).arrow_forward2. 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_forward
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