Interest rates are expressed as annualized rates for the term specified. Report your interest rate answers as fractional numbers like 0.11 for 11% per year.
Problem . The price of a stock is currently B1. The stock price by the end of the next three-month period is expected to be up by 10 percent or down by 10 percent. The risk-free interest rate is B2 percent per annum with continuous compounding. What is the current value of a three-month American call option with strike price of B3 using a single-step binomial tree? How will you trade involving one call option to make arbitrage profits if the call option's current market price is B4.
1. What is the value of p? What are the two values (cash flows) of the call option at maturity from top to bottom of the tree?
2. Cash flows at the top of the tree.
3. Cash flows at the bottom of the tree.
4. What is the current fair value of the call option?
5. What is the value of delta at time 0?
6. Write 1 if your answer is to take a long position in the call option and 0 if it is to take a short position in the call option in an arbitrage trading strategy at time zero.
7. Write the net cash position (if borrowed write with a negative sign) at time zero. Write the two net cash positions from top to bottom at the end of one step (maturity) in your trading strategy:
8. Write the net cash made as of maturity from the arbitrage trading strategy.
B1=60.94
B2=6.188
B3=55.938
B4=31.44