Question

​Eagletron's current stock price is $ $10. Suppose that over the current​ year, the stock price will either increase by 96% or decrease by 51%. ​Also, the​ risk-free rate is 25% ​(EAR).

a. What is the value today of a​ one-year at-the-money European put option on Eagletron​ stock?

b. What is the value today of a​ one-year European put option on Eagletron stock with a strike price of $19.60​?

c. Suppose the put options in parts ​(a​) and ​(b​) could either be exercised​ immediately, or in one year. What would their values be in this​ case?

Answer 1

Answer a)
Pu=	0	Pd=	5.1
delta=	(0-5.1)/(19.6-5.1)	-0.35172
B=	(5.1-5.1(-0.35172))/1.25	5.515018
Price today=	Delta* stock price +B
	1.998
Answer b)
The payoff are Pu = 0	pd=	9.6+4.9 =14.5
so 14.5/5.1	2.843137255
value should be	5.6800
Answer c)
Intrinsic value in a)=	0	so we should exercise imediately as we are getting $1.998
Intrinsic value in b)=	19.6-10=9.6	so we should exercise now