A stock has a beginning market value of $75. It can either increase in value 15%...

A stock has a beginning market value of $75. It can either increase in value 15% each year or decrease in value by 15%. A 3-year European call option written on the stock has an exercise price of $75. The risk-free rate of return is 5% per year. What is the current equilibrium price of the call option if you maintain a riskless portfolio by readjusting your relative positions in stocks and puts at the end of each year?

X=75

Payoff of call at t=3 is max [0,S_t-X]

Expert Solution

Inputs
Strike or Exercise price*	75
Current Stock Price*	75
Risk free interest rate*	0.05
Percentage Rise of Stock*	0.15
Percentage Fall of Stock*	-0.15

Outputs
Stock Price at Maturity (Rise)	=K5+K5*K7	86.25
Stock Price at Maturity (Fall)	=K5+K5*K8	63.75
Put Option Price at Maturity (Rise)	=MAX(K4-K11,0)	0
Put Option Price at Maturity (Fall)	=MAX(K4-K12,0)	11.25
Portfolio Replication
	=(K13-K14)/(K11-K12)	-0.5
	=(K14-K16*K12)/(1+K6)	41.0714285714286
Put Option Price now	=K16*K5+K17	3.57142857142857

Put option Price = 3.571287

Now as mentioned in the problem we'll use the put call parity to arrive at the call price =$ 13.78

Number of Periods to Expiration*	3.00
Strike or Exercise price*	$75.00
Stock Price*	$75.00
Call Price*	$0.00
Put Price*	$3.57
Interest rate per Period*	5.00%
Leave the unknown variable as 0 above for calculation below. Only 1 unknown variable at one time is supported.

Outputs
Stock Price + Put Price = Present value of Strike price + Call Price
Stock Price	$75.00
Put Price	$3.57
Present value of Stike price	64.78781989
Call Price	$13.78

jeff jeffy answered 1 year ago

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