Question

Use the following information for questions 18 & 19.

Bank of America (BofA) is currently selling for $30.20 and the risk-free rate is 2.75% per annum with continuous compounding for all horizons up to 9 months. BofA stock has a volatility of 30%.

1. If you are interested in pricing a 6-month European call option on BofA with a strike of $30 using a 6-step binomial tree what is the risk-neutral probability of the stock going up? (Assume you are using Cox, Ross, Rubinstein approach)

1. 0.4796
2. 0.4822
3. 0.4916
4. 0.5204
5. 0.5396

1. If you are interested in pricing a 3-month European put option on BofA with a strike of $30 using a 3-step binomial tree what is the value of u? (Assume you are using Cox, Ross, Rubinstein approach)

1. 1.0253
2. 1.0277
3. 1.0905
4. 1.0930
5. 1.1618

The answers are C for both. Can you please show the work for these questions?

Answer 1

1.
Option C

We know that in Cox, Ross and Rubinstein approach, pu=(exp(rt)-exp(-vol*sqrt(t)))/(exp(vol*sqrt(t))-exp(-vol*sqrt(t)))

As it is a three step binomial tree so each step is 1/6*6=1 month=1/12 years

=(exp(2.75%*1/12)-exp(-30%*sqrt(1/12)))/(exp(30%*sqrt(1/12))-exp(-30%*sqrt(1/12)))
=0.4916

2.
Option C
We know that in Cox, Ross and Rubinstein approach, u=exp(volatility*sqrt(t))

As it is a three step binomial tree so each step is 1/3*3=1 month=1/12 years

u=exp(30%*sqrt(1/12))
=1.090463178