The diagram shows a two-step non-recombining binomial tree. The numerical values shown are X,, the possible...
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The diagram shows a two-step non-recombining binomial tree. The numerical values shown are X,, the possible values of a particular derivative at times i = 0,1.2, based on a probability measure P that attributes equal probability to the two branches at each step. F, denotes the filtration of the derivative value process at time i. (1) (ii) 13 (b) (c) E=0 20 1=1 15 12 0 1 =2 (a) (b) (c) (d) (c) [6] The risk-neutral probability measure Q attributes probabilities of 0.4 and 0.6 to the up-paths and down-paths at each branch of this tree. (a) If X₁ = 20, what are the realised values of F, and F? What is the value of Ep(X₂ F) in this case? What is the value of Ep(X₂F) in the case where X₁ =6? Hence calculate Ep[Ep(X₂ Fi)| Fol Calculate Ep(X₂F) and comment on your answer. Does your conclusion in (i)(e) still apply when the probability measure Q is used in place of P? State briefly why this type of result is useful. Calculate the value of the derivative at time 0. presenting your calculations in the form of a tree. Ignore interest. [4] [Total 10] (i) (ii) (iii) Explain what is meant by a "complete market". Give two reasons why in practice financial markets may not be complete. [2] State the relevance of the concept of complete markets in derivative pricing. [2] [Total 6] [2] The diagram shows a two-step non-recombining binomial tree. The numerical values shown are X,, the possible values of a particular derivative at times i = 0,1.2, based on a probability measure P that attributes equal probability to the two branches at each step. F, denotes the filtration of the derivative value process at time i. (1) (ii) 13 (b) (c) E=0 20 1=1 15 12 0 1 =2 (a) (b) (c) (d) (c) [6] The risk-neutral probability measure Q attributes probabilities of 0.4 and 0.6 to the up-paths and down-paths at each branch of this tree. (a) If X₁ = 20, what are the realised values of F, and F? What is the value of Ep(X₂ F) in this case? What is the value of Ep(X₂F) in the case where X₁ =6? Hence calculate Ep[Ep(X₂ Fi)| Fol Calculate Ep(X₂F) and comment on your answer. Does your conclusion in (i)(e) still apply when the probability measure Q is used in place of P? State briefly why this type of result is useful. Calculate the value of the derivative at time 0. presenting your calculations in the form of a tree. Ignore interest. [4] [Total 10] (i) (ii) (iii) Explain what is meant by a "complete market". Give two reasons why in practice financial markets may not be complete. [2] State the relevance of the concept of complete markets in derivative pricing. [2] [Total 6] [2]
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a If X220 then the realised values of the filtrations F0 F1 F2 are F0 F1 X... View the full answer
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Business Analytics Communicating With Numbers
ISBN: 9781260785005
1st Edition
Authors: Sanjiv Jaggia, Alison Kelly, Kevin Lertwachara, Leida Chen
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