Reference no: EM132683971

Shares of XYZ-Company are currently trading at $25 and have yearly volatility 30%. A European put written on XYZ-Company shares is available for purchase. This put has strike price $22 and will mature in nine months. The continuously compounding interest rate is 7% per annum.

(a) Use the Black-Scholes model to calculate the premium of the European put.

(b) Calculate the delta for this put.

(c) A writer sells 1,000 of these European puts at the premium determined in (a). The writer wants to manage risk by using self-financing dynamic hedging:

(i) When selling the puts, should the writer buy or short sell shares? How many?

(ii) When selling the puts, should the writer borrow or deposit cash in a bank? How much?

(d) Use put-call parity to calculate the premium of the European call with the same strike price, underlying asset and time to maturity as the European put. To determine the present value of the strike, recall that the interest rate is continuously compounding.

(e) For a one-step binomial model where one time step is nine months, calculate the up factor u, the down factor d and the return R over one time-step.

(f) Typically, a premium calculated using a one-step binomial pricing model will be quite different to a premium calculated using the Black-Scholes model. How would you change the binomial pricing model to obtain a premium which is closer to the Black-Scholes model premium? (You do not have to calculate the premium with the binomial pricing model.)