3 Spreadsheet for a 12 step CRR model

Example 3.1. Assume that a 12 step CRR calibrated binomial stock model has the following parameters and assume that there are 365 days in a year:

= 0,4984.

Stock price at time 0: S0 = 429.

Continuously compounded annual risk free rate is r = 8%.

Time to maturity of all the derivatives is 231 days.

The strike of all the derivatives is K = 460.

Calculate in Excel without any rounding but give your answers rounded off to two significant decimals.

1. The length of a single time step in the 12 step model over 231 days is t = . . . . . . . . . years.

2. An up-move in the calibrated binomial CRR model is u = . . . . . . . . . .

3. A down-move in the calibrated binomial CRR model is d = . . . . . . . . . .

4. The risk-neutral probability q = . . . . . . . . . .

5. The fair price of a European call option, expiring in 231 days with an exercise price of 460 is C0 = . . . . . . . . . .

Solution.

1. t = 0,053

2. u = 1.12

3. d = 0,89

4. q = 0,49

5. C0 = 64.90

Excercise 3.1. Assume that a 12 step CRR calibrated binomial stock model has the following parameters and assume that there are 365 days in a year:

= 0,6279.

Stock price at time 0: S0 = 378.

Continuously compounded annual risk free rate is r = 7%. 5

Time to maturity of all the derivatives is 231 days.

The strike of all the derivatives is K = 440.

Calculate in Excel without any rounding but give your answers rounded off to two significant decimals.

3.1.1 The length of a single time step in the 12 step model over 231 days is t = . . . . . . . . . years. 3.1.2 An up-move in the calibrated binomial CRR model is u = . . . . . . . . . .

3.1.3 A down-move in the calibrated binomial CRR model is d = . . . . . . . . . .

3.1.4 The risk-neutral probability q = . . . . . . . . . .

3.1.5 The fair price of a European put option, expiring in 231 days with an exercise price of 440 is P0 = . . . . . . . . . .

3.1.6 The fair price of a European call option, expiring in 231 days with an exercise price of 440 is C0 = . . . . . . . . . .