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Question 1. (10 points) On January 1st, 2010, Luna entered a long position in a forward on a stock S, with maturity on January 1st,

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Question 1. (10 points) On January 1st, 2010, Luna entered a long position in a forward on a stock S, with maturity on January 1st, 2012, and S(0) = $90. On that date, it was known that the stock will pay two dividends, a $10 dividend after half a year (July 1st, 2010) and an additional $d dividend after a year and three months (April 1st, 2011). The present value of the dividends on January 1st, 2010 was $26. On January 1st, 2011, the price of the stock was S(1) = $110. Assume that the interest rate is 0.06% compounded continuously. (a) (1 points) Find d. (b) (2 points) Find the forward price on January 1st, 2010 and the forward price on January 1st, 2011. (c) (2 points) What is the value of the forward contract (which she signed on January 1st, 2010) on January 1st, 2011? (d) (5 points) An error occurred and on January 1st, 2011, the value of the long contract (that was signed on January 1st, 2010) is set to 10 dollars. Find an arbitrage opportunity that gives on January 1st 2012 exactly $30 in every scenario. Question 1. (10 points) On January 1st, 2010, Luna entered a long position in a forward on a stock S, with maturity on January 1st, 2012, and S(0) = $90. On that date, it was known that the stock will pay two dividends, a $10 dividend after half a year (July 1st, 2010) and an additional $d dividend after a year and three months (April 1st, 2011). The present value of the dividends on January 1st, 2010 was $26. On January 1st, 2011, the price of the stock was S(1) = $110. Assume that the interest rate is 0.06% compounded continuously. (a) (1 points) Find d. (b) (2 points) Find the forward price on January 1st, 2010 and the forward price on January 1st, 2011. (c) (2 points) What is the value of the forward contract (which she signed on January 1st, 2010) on January 1st, 2011? (d) (5 points) An error occurred and on January 1st, 2011, the value of the long contract (that was signed on January 1st, 2010) is set to 10 dollars. Find an arbitrage opportunity that gives on January 1st 2012 exactly $30 in every scenario

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