A 6-month 80-strike put option on a stock is selling for $3.5. The risk-free interest rate,...

 

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A 6-month 80-strike put option on a stock is selling for $3.5. The risk-free interest rate, compounded continuously, is 2% per annum. The stock has a current price of $90 and the dividend yield of the stock (also compounded continuously) is 3% per annum. All options in this question are European. (a) A 6-month 80-strike call option is also available. Calculate the price of this option using the put-call parity. [3 marks] (b) A 6-month 70-strike call option on the same stock has a price of $15, and a 6-month 90-strike call option on the same stock has a price of $7. Show that at least one of the options mentioned in this question is mispriced by constructing a portfolio that allows you to effect arbitrage using: the 70-strike call option; • the 80-strike call option in part (a); and • the 90-strike call option. Assume that you can borrow and lend at the risk-free rate and that there are no transaction costs. [5 marks] (c) Suppose the stock's annual volatility is 30%. Using a 3-period binomial tree model, calculate the price of a 6-month 60-strike call option. A 6-month 80-strike put option on a stock is selling for $3.5. The risk-free interest rate, compounded continuously, is 2% per annum. The stock has a current price of $90 and the dividend yield of the stock (also compounded continuously) is 3% per annum. All options in this question are European. (a) A 6-month 80-strike call option is also available. Calculate the price of this option using the put-call parity. [3 marks] (b) A 6-month 70-strike call option on the same stock has a price of $15, and a 6-month 90-strike call option on the same stock has a price of $7. Show that at least one of the options mentioned in this question is mispriced by constructing a portfolio that allows you to effect arbitrage using: the 70-strike call option; • the 80-strike call option in part (a); and • the 90-strike call option. Assume that you can borrow and lend at the risk-free rate and that there are no transaction costs. [5 marks] (c) Suppose the stock's annual volatility is 30%. Using a 3-period binomial tree model, calculate the price of a 6-month 60-strike call option.

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a Using putcall parity C80 P80 S Xert C80 ... View the full answer