Nyx is interested in a 4-month European call option with a strike price of $100 on...

 

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Nyx is interested in a 4-month European call option with a strike price of $100 on a share in Olympus Technologies (OMP). The current price for an OMP share is $98. Nyx has analysed past data as well as used her experience to estimate the volatility of these shares to be 25% per annum. The risk-free continuously compounding interest rate is 4% per year. a) Construct a 4-step binomial tree showing the possible share prices over the next 4 months. Also, clearly show the corresponding probabilities for an upward and a downward movement in the share price. As a check, the numbers 91.1766 and 113.2169 should appear in your tree. [3 marks] b) Suppose that one month has passed and the share price has gone UP. Using the relevant portion of your binomial tree from part a) and the information given above, calculate the corresponding 3-step binomial tree for the remaining 3 months of the option, and clearly state the fair price of the option according to the given information. [4 marks] c) Using the 3-step binomial tree constructed in part b) (i.e. today is time t = 1), estimate the values of delta (A), theta (0), and gamma (T) ONLY. You do NOT need to calculate nu (v) and rho (p). [3 marks] Nyx is interested in a 4-month European call option with a strike price of $100 on a share in Olympus Technologies (OMP). The current price for an OMP share is $98. Nyx has analysed past data as well as used her experience to estimate the volatility of these shares to be 25% per annum. The risk-free continuously compounding interest rate is 4% per year. a) Construct a 4-step binomial tree showing the possible share prices over the next 4 months. Also, clearly show the corresponding probabilities for an upward and a downward movement in the share price. As a check, the numbers 91.1766 and 113.2169 should appear in your tree. [3 marks] b) Suppose that one month has passed and the share price has gone UP. Using the relevant portion of your binomial tree from part a) and the information given above, calculate the corresponding 3-step binomial tree for the remaining 3 months of the option, and clearly state the fair price of the option according to the given information. [4 marks] c) Using the 3-step binomial tree constructed in part b) (i.e. today is time t = 1), estimate the values of delta (A), theta (0), and gamma (T) ONLY. You do NOT need to calculate nu (v) and rho (p). [3 marks]

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a To construct a 4step binomial tree for Nyxs European call option on Olympus Technologies OMP with ... View the full answer