A company share price is to be modelled using a 5-step recombining binomial tree, with each...

  

Transcribed Image Text:

A company share price is to be modelled using a 5-step recombining binomial tree, with each step in the tree representing one day. Each day, it is assumed that the share price: increases by 2%, or decreases by 1% You may assume that the force of interest is d = 5.5% pa and that there are 365 days in a year. No dividends are to be paid over the next five days. (i) Calculate the risk-neutral probability of an up-step on any given day. [2] (ii) Calculate the fair price of a 5-day at-the-money call option on £10,000 worth of shares in this company. [5] A special option is available where the payoff after 5 days is: max {S; - K.0} where S is the arithmetic average share price recorded at the end of each of the 5 days and K is the strike price. (iii) Calculate the fair price of a 5-day special option (strike price K=1.065) on £10,000 worth of shares in this company. [4] (iv) Explain whether an at-the-money special option is likely to have a higher value of vega than a standard "vanilla" call option. [3] A forward contract is arranged where an investor agrees to buy a share at time T for an amount K. It is proposed that the fair price for this contract at time t is: f(S₁,1)=S, - Ke-(T-1) Show that this: (1) satisfies the boundary condition (ii) satisfies the Black-Scholes PDE. A company share price is to be modelled using a 5-step recombining binomial tree, with each step in the tree representing one day. Each day, it is assumed that the share price: increases by 2%, or decreases by 1% You may assume that the force of interest is d = 5.5% pa and that there are 365 days in a year. No dividends are to be paid over the next five days. (i) Calculate the risk-neutral probability of an up-step on any given day. [2] (ii) Calculate the fair price of a 5-day at-the-money call option on £10,000 worth of shares in this company. [5] A special option is available where the payoff after 5 days is: max {S; - K.0} where S is the arithmetic average share price recorded at the end of each of the 5 days and K is the strike price. (iii) Calculate the fair price of a 5-day special option (strike price K=1.065) on £10,000 worth of shares in this company. [4] (iv) Explain whether an at-the-money special option is likely to have a higher value of vega than a standard "vanilla" call option. [3] A forward contract is arranged where an investor agrees to buy a share at time T for an amount K. It is proposed that the fair price for this contract at time t is: f(S₁,1)=S, - Ke-(T-1) Show that this: (1) satisfies the boundary condition (ii) satisfies the Black-Scholes PDE.

Answer rating: 100% (QA)

1 To calculate the riskneutral probability of ... View the full answer