Question

The price of a stock is currently $39.38. 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 1.875 percent per annum with continuous compounding. What is the current value of a three-month European call option with strike price of $34.375 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 $9.88?

23. 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?

24. Cash flows at the top of the tree.

25. Cash flows at the bottom of the tree.

26. What is the current fair value of the call option?

27. What is the value of delta at time 0?

28. 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.

29. 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:

30.

31.

32. Write the net cash made as of maturity from the arbitrage trading strategy

Answer 1

N is no. of years

Rf risk free rate

Exponential is e to the power of rf * n of times

n	0.25
Rf	1.875	p.a. continuous
Exercise price	34.375
Rf monthly	0.15625		43.318	Value	8.943
exponential number	0.039063	0.5
Stock price	39.38
		0.5
			35.442	Value	1.067
Value of call	0.5 * 8.943 disc at rf for 3 months + ).5 * 1.067 disc at rf for 3 months
exponential fig	1.039835
Value at Upper node	4.649624
Value at lower node	0.554752
Value of call	5.20
Current Value	9.88
Arbitrage Profit	4.68
We should sell the call at market and buy the option & wait for 3 months
Sold a call cash flow received 9.88 and outfloe of premium paid - 5.20
Resulting in arbitrage profit of 4.68 at the end of 3months