a 1-year European call option on stock A Stock A has current price $10. At the end

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Question:

a 1-year European call option on stock A Stock A has current price $10. At the end of the year, the stock price will either be $15 (with 50% probability) or $10. The strike price of the option is $10.

a 1-year European call option on stock B Stock B has current price $10. At the end of the year, the stock price will either be $14 (with 50% probability) or $5. The strike price of the option is $10.

The riskless interest rate is 10% per year and the riskless bond sells for $1.

1. Calculate the price of the call options on stocks A and B. Which call option is worth more?

2. Consider two put options with the same exercise prices as the calls on Stocks A and B. Calculate their prices. Which of these is worth more?

3. What is the expected level and volatility of the stock price?1In this light, comment on your finding in parts (a) and (b).

Assume that the two stocks (and their respective derivatives) exist in segmented markets so that arbitrage opportunities between them or between derivatives written on them cannot be exploited. In other words, Stock B may not be used to create a portfolio that replicates the payoffs of a derivative written on stock A. Similarly, stock A may not be used to create a portfolio that replicates the payoffs of a derivative written on stock B.

1 Recall that if the stock price is x1 with probability p1 and x2 with probability p2 (where p1 + p2 =1), then Expected price of the stock is = E[x] = p1x1 + p2x2 Variance of stock price = p1 (x1 -E[x])2 + p2 (x2 - E[x])2 and volatility of the stock price is the square root of its variance.