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##### GMBA 767-Security Analysis and Portfolio Management Problems

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**Question**

Question;5. Consider the following questions on the pricing of;options on the stock of ARB Inc.;a- A share of ARB stock sells for $75 and has a standard;deviation of returns equal to 20% per year. The current risk-free rate is 9%;and the stock pays two dividends: (1) a 2% dividend just prior to the option?s;expiration day, which is 91 days from now (i.e., exactly one half year).;Calculate the black-Scholes value for European-style call option with an;exercise price of $70.;b- What would be the price of a 91-day European-style option;on ARB stock having the same exercise price?;c- Calculate the change in the call option?s value that;would occur if ARB?s management suddenly decided to suspend dividend payments;and this action had no effect on the price of the company?s stock.;d- Briefly describe (without calculations) how your answer;in part a would differ under the following separate circumstances: (1) the;volatility of ARB stock increases to 30%, and (2) the risk free rate decreases;to 8%.;10- Melissa Simmons is the chief investment officer of a;hedge fund specializing in options trading. She is currently back testing;various option trading strategies that will allow her to profitfrom large;fluctuations-either up or down-in a stock?s price. An example of such typical;trading strategy is straddle strategy that involves the combination of a long;call and a long put with an identical strike price and time to maturity. She is;considering the following pricing information on securities associated with;friendwork, a new internet start-up hosting a leading online social network;Friendwork stock: $100;Call option with an exercise price of $100 expiring in one;year: $9;Put option with an exercise price of $100 expiring in one;year: $8;a. Use the;above information on friendwork and draw a diagram showing the net profit/loss;position at maturity for the straddle strategy. Clearly label on the graph the;break-even points of the position.;b. Melissa?s;colleague proposes another lower-cost option strategy that would profit from a;large fluctuation in friendwork?s stock price;Long call option with an exercise price of $110 expiring in;one year: $6;Long put option with an exercise price of $90 expiring in;one year: $5;Similar to part a, draw a diagram showing the net;profit/loss position for the above alternative option strategy. Clearly label;on the graph the breakeven points of the position.

Paper#48928 | Written in 18-Jul-2015

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