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Suppose you want to speculate using call options. To do so, you form a

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Option Theory Problems;1. Suppose you want to speculate using call options. To do so, you form a long straddle by buying a call;(Premium = $5) and buying a put (Premium = $3), where both options have the same 1-year maturity and the;same $50 exercise price. a) Draw a graph showing the profits from the two-option portfolio as a function of;the underlying assets price. In particular, explicitly show the numerical profits for ST = 0 and ST = X.;2. Compute the price of a European call option with the following parameter values: S = $220, X = $200;r = 5% p.a., = 30%, T = 6 months. You may use the normal table, and use the closest value in the table to;the number that you are looking for. In other words, you need not interpolate.;3. Compute the price of a European call option with the following parameter values: S = $220, X = $200;r = 5% p.a., = 30%, T = 12 months. You may use the normal table, and use the closest value in the table;to the number that you are looking for. In other words, you need not interpolate.;4. What do problems 2 and 3 illustrate regarding the relationship between option prices and time to maturity?;5. Compute the price of a European call option with the following parameter values: S = $200, X = $200;r = 6% p.a., = 40%, T = 9 months. You may use the normal table, and use the closest value in the table to;the number that you are looking for. In other words, you need not interpolate.;6. Compute the price of a European call option with the following parameter values: S = $200, X = $160;r = 6% p.a., = 40%, T = 9 months. You may use the normal table, and use the closest value in the table to;the number that you are looking for. In other words, you need not interpolate.;7. What do problems 5 and 6 illustrate regarding the relationship between option prices and strike price?;8. You buy a put option and sell the corresponding call option. Both options have an exercise price of $100.;In addition, you also buy 1 share of IBM stock. What is the net payoff you receive from this 3-asset portfolio;if at expiration the price of each share of IBM stock is a) $120, b) $12. You must draw the relevant graph.;9. A put option expires in the money. What is the payoff at expiration of the corresponding call option, that;is, a call written on the same stock and with the same maturity and exercise price as the put option?;10. A 1-year put option and a 1-year call option have the same underlying stock and the same exercise price.;If the current price of the underlying stock is equal to the present value of the exercise price, find the exact;relationship between the price of the call option, C, and the price of the put option, P (e.g., the relationship;may be something like P = 5C2 + 2/C);11. Suppose you want to speculate using call options. To do so, you form a short straddle by selling a call;(Premium = $8) and selling a put (Premium = $6), where both options have the same maturity (T=1 year) and;the same exercise price (X=$100). a) Draw a graph showing the profits from the two-option portfolio as a;function of the underlying assets price. b) What are the numerical values of the profits for ST = 0 and ST =;X? c) Which price(s) of the underlying asset produce zero profits? d) Whats the minimum possible profit? e);Whats the maximum possible profit? (Note: remember that profits can also be negative.);12. Compute the price of a European put option with the following parameter values: S = $28, X = $30;r = 6% p.a., = 30%, T = 15 months. You may use the normal table to find the closest value to the number;that you are looking for. In other words, you need not interpolate.;13. Give a convincing and SIMPLE argument for the fact that the price of a put must be less than the present;value of the exercise price, that is, P < Xert. (Note: for the record, less really means less than or equal to;though this technicality should have no effect on your argument.);14. Use the NORM.S.DIST function in Excel to create a cumulative standard normal distribution table;identical to the one in your notes (except for styling and color), from 0.00 to 3.49. Do it carefully, as you will;be allowed to bring a hard copy of this table to the upcoming exams. Note: You only need to input in Excel a;formula in one cell (the one for 0.00), and then copy it to all the other cells. Youll need to reference the;numbers in the leftmost column (0.0, 0.1,,3.4) and the numbers in the uppermost row (0.00, 0.01,, 0.09);within the formula, so be careful to correctly use the absolute reference symbol ($) in your formula. The table;should be in a separate page of your report, and should occupy the entire page (allow for a reasonable margin).

 

Paper#26463 | Written in 18-Jul-2015

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