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##### 1. Discuss the limitations of Black?Scholes option...

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**Question**

1. Discuss the limitations of Black?Scholes option pricing formula. 2. Consider options on a non?dividend?paying stock when the stock price is $100, the strike price is $95, the risk?free interest rate is 2% per annum, the volatility is 25% per annum, and the time to maturity is 7 months. a. Price a European call option. Do not use Derivagem. b. If the option is an American call instead of a European call, will the call holder ever early exercise the option before expiration? (hint: Chapter 10, Section 5) Will the American call price be the same or different from part a. Explain. c. Price a European put option. Do not use Derivagem. d. If this is an American put, will the price be the same or different from part d? Explain. e. Use Derivagem to answer parts a and c. Copy paste the DG outputs to show that the prices are identical. f. Verify that put?call parity (Eq. 10.6) holds using your answers above. This is not a yes or no question. You must calculate both sides of the equation and show that the put?call parity holds. g. Suppose the European call is currently trading at $15. Calculate the implied volatility. Include the DG output. 3. What is VIX index? Suppose you expect the stock market volatility will greatly increase in the near future. With such expectation, how will you invest in VIX futures? 4. Use the Black?Scholes pricing to fill out the following table with ?+? or ???. + means the higher value of the variable increases the option price. ? means the variable has a negative effect on the option price. (You don?t have to include DG outputs for this question.) Variable European call price European put price current stock price strike price volatility risk?free rate dividends 5. A call option on a non-dividend-paying stock has a market price of $2.50. The stock price is $15, the exercise price is $13, the time to maturity is three months, and the risk-free interest rate is 5% per annum. What is the implied volatility? 6. Consider an American call option on a stock. The stock price is $70, the time to maturity is eight months, the risk-free rate of interest is 10% per annum, the exercise price is $65, and the volatility is 32%. A dividend of $1 is expected after three months and again after six months. Use the results in the appendix to show that it can never be optimal to exercise the option on either of the two dividend dates. Use DerivaGem to calculate the price of the option.

Paper#2759 | Written in 18-Jul-2015

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