Question

The current price of a stock is $48. In 1 year, the price will be either $55 or $31. The annual risk-free rate is 6.6%. Find the price of a call option on the stock that has a strike price of $50 and that expires in 1 year. ( Use daily compounding.)     

                   
                     Inputs                      
P0   = ?    u   = ?
X = ?    d   = ?
                      
Cu   = ? Pu   = ?
Cd   = ? Pd   = ?

Use the Binomial Model 4-step approach
Step 1	Ns	=
Step 2	Payoff	=
Step 3	PV(payoff)	=
Step 4	Price for N shares		=
	Vc	=

Use the Binomial Model Formula Approach (single-period, thus n=1)
	ert/n	=
	πu	=
	πd	=
	Vc	=

Use the same Binomial Formula to price an option with the same chararistics but with strike price of $45.
	Cu	=
	Cd	=
	Vc	=

   
                          
                          
                          

Answer 1

as per binomial model binomial refers to two value a stock can take at the end of the period.

in this approach the assumpion is that investing in such stock to have the risk of invesing in a risk free asset. since we are assuming investing in such a stockand investing in risk free asset to be of same rik, they should giv same rate.

mathamaticlly p*Cu+(1-p)Cd=S*e^rt

p= probbiity

Cu=above the stock price

Cd=below the stock price

s=stock current price

value of call= present value of (p*Cu+(1-p)Cd)

here cu= max(cu-x,0)

cd=max(cd-X,0)

value of put =present value of (p*Cu+(1-p)Cd)

here cu=max(x-cu,0)

cd=max(x-cd,0)

soution to the problem are attached below.