Assignments - Winter 2012

- Chapter 18, Problems 2 and 3. Calculate the Delta in problem 3 two ways: using our formula, and comparing how the option price changes if the stock price increases by 0.0001
- Chapter 14, Problem 27 [volatility estimate only]

Solutions

- Chapter 12, problems 17(b), and 19 [American option portion]
- Refer to Assignment 3, problem B part (b).
- Work out the price if this option is American rather than European.
- Identify all nodes of the tree at which early exercise is optimal.

- Refer to Assignment 4, Problem 4(b), but take the dividend yield to be
q=5%, and take the option to be an American call.
- Describe the arbitrage if the call trades for $2.70 and the stock evolves as up/up/up, and the option isn't exercised early.
- Describe the arbitrage if the call trades for $2.00 and the stock evolves
as up/up/up.

[Note: the original question had $2.40 here, but that was because I made a numerical mistake. If you have already done this question using $2.40, that's fine - I will accept that. If you haven't done it yet, please use $2.00, which is the number I will use in the solutions.]

Solutions, with accompanying spreadsheet

All questions were graded. The problems were worth 10/10/15/15 respectively, for a total of 50.

Solutions, with accompanying spreadsheet

All questions were graded. The problems were worth 10/10/15/20 respectively, for a total of 55

- Chapter 12: Problems 17(a), 19 [European only]. In each case, state the risk neutral probability of an up-move.
- Chapter 13: Problem 17
- Chapter 14: Problem 26
- Problem A: You own a European option on a stock. The stock has an expected
return of 12%, a volatility of 20%, and a current price of $100.
What is the probability the option will be exercised if:
- (a) It is a call with strike $130 maturing in 6 months?
- (b) It is a put with strike $95 maturing in 18 months?

- Problem B: Using software (Hull's, Excel, or something else), build a 6
period tree for option pricing. Apply it to obtain a price in the following
situations.
- (a) European call, R=1.01, u=1.05, d=.95, strike =$40, current stock price =$50
- (b) European put maturing in 18 months, calibrated (using formulas 12.13 and 12.14 of Hull) to a stock with volatility 25%. Assume the risk free rate is 3%, the strike is $50, and the current stock price is $55.
- (c) As in (b) but now for a "binary" option that pays $20 if the price in 18 months is $20 or more, and pays $0 otherwise.

All questions were graded. Total points: 65

- Chapter 10: Problems 22, 23
- Chapter 11: Problems 20, 22, 24, 25

Total marks: 60. All questions were graded.

- Chapter 1: Problems 28, 30, 31
- Chapter 5: Problems 25, 27, 30
- Chapter 7: Problem 21

Total marks: 60. All questions were graded except 1.31

Note that there was an issue with the grading of 5.30, regarding the frequency of compounding. If you lost marks for that and want me to look it over, then pass the assignment back to me.