Exercise 5.2. Consider a one-step market consisting of a bond and a stock. The price of The stock is £8 initially and can rise or fall by £1 at each time step. The bond has interest rate r = 5%. i. Calculate the price of a European call option on this stock with a strike price of £7.50. ii. Now consider a two-step market with the stock price rising or falling by £1 at each step. Calculate the price of this European call option at time 0. Will the risk-neutral probabilities at both steps be the same? Why? It would be helpful to draw a tree.

Exercise 5.2. Consider a one-step market consisting of a bond and a stock. The price of The stock is £8 initially and can rise or fall by £1 at each time step. The bond has interest rate r = 5%. i. Calculate the price of a European call option on this stock with a strike price of £7.50. ii. Now consider a two-step market with the stock price rising or falling by £1 at each step. Calculate the price of this European call option at time 0. Will the risk-neutral probabilities at both steps be the same? Why? It would be helpful to draw a tree.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider a one-step market consisting of a bond and a stock. The price
of The stock is £8 initially and can rise or fall by £1 at each time step. The bond has
interest rate r = 5%.
i. Calculate the price of a European call option on this stock with a strike price of
£7.50.
ii. Now consider a two-step market with the stock price rising or falling by £1 at
each step. Calculate the price of this European call option at time 0. Will the
risk-neutral probabilities at both steps be the same? Why?
It would be helpful to draw a tree.

Exercise 5.2. Consider a one-step market consisting of a bond and a stock. The price
of The stock is £8 initially and can rise or fall by £1 at each time step. The bond has
interest rate r = 5%.
i. Calculate the price of a European call option on this stock with a strike price of
£7.50.
ii. Now consider a two-step market with the stock price rising or falling by £1 at
each step. Calculate the price of this European call option at time 0. Will the
risk-neutral probabilities at both steps be the same? Why?
It would be helpful to draw a tree.

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