Question

The current price of a stock is $80, and at the end of one year its price will be either $88 or $72. The annual risk-free rate is 3.0%, based on daily compounding. Based on the binominal model, what is the present value for a 1-year call option on this stock with an exercise price of $86?

Answer 1

Particulars	Amount
Stock Price	$   80.00
Strike Price	$   86.00
Risk Free Rate per period	3%
Upside	1.1000
Down Side	0.9000
No. of Years Per period	1

Risk Nuetral prob to go Up = P
Risk Nuetral prob to go Up = ( 1 - P)
e^rt Calculation:
e^rt = e^0.03 * 1
= e^0.03
= 1.0305

P = [ e^rt - d ] / [ U - d ]
= [ 1.0305 - 0.9 ] / [ 1.1 - 0.9 ]
= [ 0.1305 ] / [ 0.2 ]
= 0.6523

( 1 - P ) = 1 - 0.6523
= 0.3477

Value of Call at the end of one period:

Today	Period1	Prob	Vc	Exp Vc
	$   88.00	0.6523	$      2.00	$      1.30
$   80.00
	$   72.00	0.3477	$          -	$          -
Vc after One Period			$      1.30

PVF at continous Rate: e^-rt
= 1 / e^(r * 1)
r - Rate per period
e - Exponential Value
= 1 / e^ (0.03* 1 )
= 1 / e^ (0.03 )
= 1 / (1.0305 )
= 0.9704

Vc Today:
= Vc after two periods * e^-rt
= $ 1.3 * 0.9704
= $ 1.27