Stock ABC and Stock XYZ have the same current price of $50, and they offer the s

Question

Stock ABC and Stock XYZ have the same current price of $50, and they offer the same distribution of future returns (with the same expected return and the same standard deviation). There exists a call option on one share of Stock ABC and a call option on one share of Stock XYZ. The options have identical exercise prices of $49 and they expire on the same date. The call premium on each option is $3.

Assume that there is a third call option, based on the average price of Stocks ABC and XYZ, with the same expiration date as the first two options. The exercise price of this option is $49. Should the price (call premium) of the third option be higher than, lower than, or equal to the prices of the two options on the individual stocks in the following two cases? (Briefly explain your answer in each case).

The correlation between the returns of the ABC and XYZ is +1

The correlation between the returns of the two stocks is +0.3

Explanation / Answer

Normally Correlation is a measure to check close relation between two random variables and is denoted with in range +1 to -1

+1 correlation is best correlation it means that both variables move in same direction with same value & -1 correlation is shows that both variables move opposite direction with same value.

Call premium is $3

Excise price is $49

1. Correlation between the return of ABC & XYZ is +1, it means both security moves with same direction with same value in the market hence in that case same excise price & same call option premium is correct because both security have correlation of +1

2. Correlation between the return of ABC & XYZ is +0.3, it means both security moves with same direction but not with same value, if ABC moves 1 % then XYZ moves 0.3 % i.e. always lower then ABC but with same direction. hence in that case Option excise price & Option premium price must be different. XYZ stock price of option excise & option premium must be lower the Stock of ABC because ABC is more fluctuating then stock XYZ

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