Question

You are given the following information on two European call options written on stock XYZ at a strike of 175.

	Maturity 11/16/2018 price	Maturity 01/17/2020 price	XYZ price
4/11/2018	12.50	20.10	178.10
4/12/2018	9.75	17.50	172.55

Assume an annual rate of interest of 2% and an annual dividend rate of 1%. Both rates are continuously compounded.

a)Compute the implied volatilities of both options on both dates. (You will compute four implied volatilities in total).

b)Create a P&L explanation for these two options. A P&L explanation is an explanation of the change in the option value between the two days. The change in value should be expressed as a function of delta, gamma, vega and time decay.

c)Discuss the main differences between the P&L explanations of the two options.

Please show all work and label the answer

Answer 1

his is a case of Black schole model of Option valuation ,

Where Strike price of XYZ call option with two different maturity is given. with two time interval as well for

4/11/2018 = value ot T 0.5972

4/12/2018 = value ot T 1.7667

Answer a)

Clealy explained with change of time the value of Option changes ,Lower the time tomaturity ,less will be the value of call option

	Inputs
	Option Type: 1=Call, 0=Put	1	1	1	1
	Stock Price Now (Ps)	178.1	172.55	178.1	178.1
	Riskfree Rate - Annual (R)	0.02	0.02	0.02	0.02
	Exercise Price (E)	175	175	175	175
	Time To Maturity - Yrs (T)	0.597222	0.594444	1.766667	1.763889
	Dividend yield (d)	0.01	0.01	0.01	0.01
	Observed Option Price	81	66.25	46	31
	Outputs
	d1	0.217557	0.063502	0.268259	0.265854
	d2	0.016369	-0.14262	-0.03887	-0.0168
	N(d1)	0.586113	0.525317	0.60575	0.604824
	N(d2)	0.50653	0.443294	0.484496	0.493298
	Model Call Price (Vc)	16.17482	13.44661	24.15146	22.50093
With Change of 2 days	Model Call Price (Vc)	16.10615	13.37715	24.1157	22.46753
	% change	-0.4246%	-0.5165%	-0.1480%	-0.1484%

Answer b) P&L value shown in above table in bold ,

Answer c)

The change in the call option value is very sharp in first option in comparision to second option of the question.