FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at 50 and will be either 60 or 40 after one year. The risk-free rate is 5% per year with annual compounding. A trader replicates a one-year European call with strike 50 using shares and borrowing. How much must be borrowed today?
The trader must borrow 19.05. The replicating portfolio holds 0.5 shares, and in the down state the shares are worth 20, which equals the loan repayment. Discounting 20 at 5% gives 19.05 borrowed today. Borrowing 20 ignores the time value of money.
- A19.05Correct
- B20.00
- C25.00
- D5.95
Explanation
The call pays 10 if the stock is at 60 and 0 if it is at 40, so delta = 10/20 = 0.5 shares. In the down state the replicating portfolio must be worth 0, so 0.5 × 40 = 20 must be repaid, and the amount borrowed today is 20/1.05 = 19.05. Check: the call value is 0.5 × 50 - 19.05 = 5.95, which matches 0.625 × 10 / 1.05. The 20.00 option forgets to discount the repayment.
Did you get it right without looking?
One question tells you little. A timed set on Binomial Trees shows your real accuracy, how long you take and where you lose marks.
More Binomial Trees questions
- A stock is at 100 and in one period will move to either 110 or 90. A European put option with a strike price of 105 expires at the end of th…
- A stock is at USD 40 and in six months will be USD 44 or USD 36. A six-month European call has a strike of USD 40, and the risk-free rate is…
- A stock trades at 50. Over one year it moves up by a factor of 1.2 or down by a factor of 0.8 in a single-step tree. The continuously compou…
- A two-step tree has S0 = 100, u = 1.1 and d = 0.9. The risk-neutral up probability is 0.6 and the per-step discount factor is 0.96. Using ba…
- A stock is priced at USD 100. In one year it will be either USD 120 or USD 80. The continuously compounded risk-free rate is 5%. Using risk-…
- A stock has an annual volatility of 30%. An analyst builds a Cox-Ross-Rubinstein binomial tree with time steps of 0.25 years. What is the up…