t2-370-07-sol - ACT370H1S - TEST 2 - MARCH 28, 2007 Write...

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ACT370H1S - TEST 2 - MARCH 28, 2007 Write name and student number on each page. Write your solution for each question in the space provided. Calculations should be done to 6 decimal places and displayed to 4 decimal places. 1. Today's exchange rate between Canadian and US currency is $1US $1.2000CDN . œ A binomial model for exchange rates has and each year for the next 2 years. ? œ "Þ" . œ Þ* The annual effective risk free rate of interest in the US is 6% each year for the next 2 years, and in Canada it is 4%. (Hint: Remember that the foreign interest rate behaves like a continuous dividend on the fore gin currency). 4 (a) Construct the 2 year (2 step binomial tree for the $US in terms of $CDN and show that the risk neutral probability of an up-step at any node in the tree is .405660. Verify that the exchange : rate at time 0 is consistent with the risk-neutral expected present value of the three possible outcomes at time 2. 4 (b) Find the value today of a European call option to purchase $1US two years from now at a strike price of $1.20CDN. Indicate the amount of $US and the amount of risk-free investing or borrowing in the replicating portfolio at time 0. 4 (c) Find the value today of an American call option to purchase $1US two years from now at a strike price of $1.20CDN. 4 (d) Find the value today of a European put option to purchase $1US two years from now at a strike price of $1.20CDN. Verify the put-call parity relationship between this put price and the call price in part (b).
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8 2. The price of gold today is $600 per ounce. The risk free interest rate is annual effective 10%. A binomial model for the price of gold has a value of gold one year from now of either $700 or $620. A European call option on a forward contract for delivery of an ounce of gold 2 years from now has an expiry date of 1 year from now. The option strike price is $700 (for a forward contract with delivery at time 2). A replicating portfolio for the option is created using ounces ? of gold and in risk free investing or borrowing. Determine and , and find the value of the FF ? option today.
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3. A non-dividend paying stock has annual volatility of and a current price of 100. 5 œÞ# Risk free interest is a continuously compounded rate of .
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This note was uploaded on 09/27/2009 for the course STA ACT370 taught by Professor Broverman during the Spring '07 term at University of Toronto- Toronto.

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t2-370-07-sol - ACT370H1S - TEST 2 - MARCH 28, 2007 Write...

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