Question

Answer the following questions given the following call option prices on Google (GOOG) and on Apple (APPL). Note that these are actual option prices on 2/21/13 and these contracts have 60 days till expiration. The 2-month T-bill rate is about 4.75%. Attach all work with your report.

OPTION	STRIKE	EXP	VOL	LAST
GOOG	800	APR	378	28.20
S=795.53	690	APRI	53	101.57
APPL	450	APR	530	18.55
S=446.06	480	APR	856	7.81

Part One

Estimate the theoretical option values for the call on GOOG with K =800 and for the call on APPL with K = 450 using the Black-Scholes-Merton and Binomial Models program available under Files, or you can use the following website to calculate option prices and implied volatility www.option-price.com (Links to an external site.) Links to an external site.

When estimating the option values assume various standard deviations of returns of 10%, 15%, 20%, … up to 100% or until you find the theoretical option value is close to the actual one.

Draw a graph showing the relationship between standard deviations and option values.

Based on the graph, what does the actual option value imply about the expected future standard deviation (volatility)? Which option has higher implied volatility and is it surprising?

Part Two

Estimate the historical standard deviation of GOOG*.

Compare the implied standard deviation with the historical standard deviation.

What can you infer from the difference, if any, between the two numbers?

Part three

Compute the implied volatility for all options.

Do you have the same implied volatility for the two options on the same underlying? If not (in which case it is referred to as volatility smile), what might be able to explain the differences?

Answer 1

Part One :

Using the given website (www.option-price.com) the Theoretical Option Values are as follows :

GOOG :

Put various figure as follows and change value in volatility box as 10, 15, 20, 25, 30.

Graph :

The Actual option value is 28.20 which implies that the Expected volitality will be around 22%.

APPL :

The Actual option value is 18.55 which implies that the Expected volitality will be around 26%.

APPL has higher Implied volatility and it is surprising.