Assume that a 3-step binomial stock model has the following parameters: u = 1.2 d = 1
Question:
Assume that a 3-step binomial stock model has the following parameters:
u = 1.2
d = 1 u
Stock price at time 0: S0 = 150
Time to maturity of all the derivatives is 6 months
Continuously compounded annual risk free rate is r = 5%.
Calculations in Excel without any rounding but give your answers rounded off to two significant decimals.
1. The length of a single time step in a 3 step model over half a year is t = . . . . . . . . . years.
2. The risk-neutral probability q is . . . . . . . . . .
3. The fair price of a European put option, expiring in six months with an exercise price of 160 is P0 = . . . . . . . . . .
4. The fair price of a European call option, expiring in six months with an exercise price of 160 is C0 = . . . . . . . . . .
5. The fair price of an American call option, expiring in six months with an exercise price of 160 is C0 = . . . . . . . . . .
Solution.
1. t = 1 6 = 0,1667 years
2. q = 0,48
3. Fair price of the European put option is P0 = 23,54
4. Fair price of the European call option is C0 = 17,49
5. Fair price of the American call option is 17,49.
Example 2.2. Assume that a 3-step binomial stock model has the following parameters:
u = 1.15
d = 1 u
Stock price at time 0: S0 = 155
Time to maturity of all the derivatives is 9 months
Continuously compounded annual risk free rate is r = 6%.
Calculations in Excel without any rounding but give your answers rounded off to two significant decimals.
1. The risk-neutral probability q is . . . . . . . . . .
2. The fair price of an American put option, expiring in nine months with an exercise price of 160 is . . . . . . . . . .
Solution.
1. q = 0,5190
2. Fair price of the American put option is 15,3982.
Excercise 2.1. Assume that a 3-step binomial stock model has the following parameters:
u = 1.1
d = 1 u
Stock price at time 0: S0 = 140
Time to maturity of all the derivatives is 9 months
Continuously compounded annual risk free rate is r = 4%. 4
Calculations in Excel without any rounding but give your answers rounded off to four significant decimals.
2.1.1 Is the model arbitrage-free? Motivate your answer.
2.1.2 The length of a single time step in the 3 step model over 9 months is t = . . . . . . . . . years. 2.1.3 The risk-neutral probability q is . . . . . . . . . .
2.1.4 The fair price of a European put option, expiring in 9 months with an exercise price of 160 is P0 = . . . . . . . . . .
2.1.5 The fair price of a European call option, expiring in 9 months with an exercise price of 160 is C0 = . . . . . . . . . .
2.1.6 The fair price of an American call option, expiring in 9 months with an exercise price of 160 is . . . . . . . . . .
2.1.7 The fair price of an American put option, expiring in 9 months with an exercise price of 160 is . . . . . . . . . .
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill