Question

Suppose that there are two possible states of the economy, A and B, in year T. A stock’s price in year T will depend on the economic state as in the table below. A risk-free bond currently sells for $8 and it will pay $10 in year T in every state.

	state a	state b
stock	$150	$80
bond	$10	$10

In addition, we also see a year-T European call option on the stock above. The call has the strike price of $100 and currently sells for $20. What is the current stock price?

Answer 1

Information given is

Year -T Call option at Strike Price of $100 currently selling at $ 20

Stock Price in Year T would be $150 & $80 in economic state A & State B respectively.

Current market price of risk free bond is $8

Market price of risk free bond in year T is $10

Note1:

Hence discount rate for up to the period of Year T is i.e. 25%

10-8 s一*100

Note 2:

Calculation of Probability of Stock price in Year T of $150

P = CMP(1+r) - S2 S1 - S2

where r is discount rate, S1 is high price & S2 is low price

PE CMP(1+.25) - 80 150 – 80

P = CMP(1+.25) - 80 70

Solution:

Calculation of Fair OP of Call using the risk neutral approach

Stock price as on Year T	Strike Price	Fair OP of Call as on Year T	Probability	Expected Fair OP of Call as on Year T
150	100	50	( note 1) CMP(1+.25) - 80 70	CMP(1+.25) - 80 50 *
80	100	0	CMP(1 +.25) - 80 1- 70	0
Total			1	CMP(1+.25) - 80 50 *

Hence the Fair OP of Call as on Year T =

CMP(1+.25) - 80 50 *

Thus PV of Fair OP of Call (i.e. Fair OP of call as on today) =

FairPof Callason Year (1+r)

CMP(1+.25) - 801 20 = 50 * (1+.25) 70

On solving equation we get CMP = $92