Question

Use a three-period CRR binomial model (meaning three jumps total up or

down in the underlying) to price a European call option for a stock whose

share price today is S = 16 when the interest rate is r = 4%, the maturity

date is 6 months (so T = .5 in years), the strike price is K = 17.5 and the

volatility is ? = 20% = .2. ,u=e(?*sqrt(T/N)). d=e(-?*sqrt(T/N))
Using put-call parity, price a corresponding put option as well.

Answer 1

For calculating Call option Price , Binomial tree is as follows:

Let the probablity of S1 be p

Calculation of Probablity = p = CMP(1+.04)- S2 / S1-S2 = (16(1+.04) -12.8) / 19.2 -12.8

= (16.64-12.8) / 6.4 = 60%, where S1 is higher price & S2 is lower price,

thus the probablity of S1 is 100%-60% =40%

CMP on Expiry (From Image above)(A)	Exercise price(B)	Call Buyer will exercise or not	Option Price(A-B)	Probality(Chain Probablity)	Value (OP*Prob.)
27.648	17.5	Yes	10.148	0.216	2.191968
18.432	17.5	Yes	0.932	0.144	0.134208
18.432	17.5	Yes	0.932	0.144	0.134208
18.432	17.5	Yes	0.932	0.096	0.089472
12.288	17.5	No	-	0.144	0
12.288	17.5	No	-	0.096	0
12.288	17.5	No	-	0.096	0
8.192	17.5	No	-	0.064	0
				Option Price	2.549856

PV value of OP = 2.549856 * PVF (4%, 3period)

=2.266813

Now using put call parity theory to calculate value of put option,

According to PCPT,

OP of call + Excercise price today = CMP as on today + OP of Put

:- 2.266813 + 17.5*PVF(4%,3peiod) = 16 + OP of Put

:- OP of Put = 1.82425