There are two securities in the market: a risky asset (stock) whose price at time t...
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There are two securities in the market: a risky asset (stock) whose price at time t is S(t) and a bond whose value at time t is B(t). Trading only takes place now at time t = 0 and payoffs are revealed at maturity T. The bond costs $1 now and pays $(1 + R) at maturity, where R is the one-period discretely compounded riskless return. The asset costs So now and can take M possible values at maturity T. The actual probability of the stock price S(T) taking values s; > 0 is p > 0, for j = 1,..., M and Σj=1 Pj = 1. For simplicity we assume that s₁ s2 <...< SM. M A straddle with strike price K > 0 and maturity T is a contingent claim written on asset S with the following maturity payoff function g(.) g(S( [S(T) – K, if S(T) ≥ K, K – S(T), if S(T) < K. a) A portfolio containing stocks and bonds is constructed to replicate the payoff of a straddle. Write down the conditions this portfolio must satisfy. b) Is it always possible to find such a portfolio? c) Using the put-call parity show that a straddle can be perfectly replicated using call options, stocks and bonds. Now assume that M = 2, So= $100, $₁ = $95, $2 = $105, R = 3%, P₁ = 50%, K = $99, T = 1 d) Compute the replicated portfolio for the straddle. Compute the value of the staddle at time period t = 0, under the assumption of no-arbitrage. e) Calculate 91 and 92 and compare them to P1 and P2. Use 91 and q2 to compute the value of the straddle at time t = = 0. Compare this value to the value obtained using the no-arbitrage principle. (Total for Question 26: 25 marks) 3 marks 2 marks 5 marks 6 marks 9 marks There are two securities in the market: a risky asset (stock) whose price at time t is S(t) and a bond whose value at time t is B(t). Trading only takes place now at time t = 0 and payoffs are revealed at maturity T. The bond costs $1 now and pays $(1 + R) at maturity, where R is the one-period discretely compounded riskless return. The asset costs So now and can take M possible values at maturity T. The actual probability of the stock price S(T) taking values s; > 0 is p > 0, for j = 1,..., M and Σj=1 Pj = 1. For simplicity we assume that s₁ s2 <...< SM. M A straddle with strike price K > 0 and maturity T is a contingent claim written on asset S with the following maturity payoff function g(.) g(S( [S(T) – K, if S(T) ≥ K, K – S(T), if S(T) < K. a) A portfolio containing stocks and bonds is constructed to replicate the payoff of a straddle. Write down the conditions this portfolio must satisfy. b) Is it always possible to find such a portfolio? c) Using the put-call parity show that a straddle can be perfectly replicated using call options, stocks and bonds. Now assume that M = 2, So= $100, $₁ = $95, $2 = $105, R = 3%, P₁ = 50%, K = $99, T = 1 d) Compute the replicated portfolio for the straddle. Compute the value of the staddle at time period t = 0, under the assumption of no-arbitrage. e) Calculate 91 and 92 and compare them to P1 and P2. Use 91 and q2 to compute the value of the straddle at time t = = 0. Compare this value to the value obtained using the no-arbitrage principle. (Total for Question 26: 25 marks) 3 marks 2 marks 5 marks 6 marks 9 marks
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Answer rating: 100% (QA)
a The portfolio must satisfy the condition that its payoff at time T is equal to the payoff of the straddle In other words the portfolio must replicate the straddles maturity payoff function which is ... View the full answer
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
Posted Date:
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