Question

1 Approved Answer

Posted on Jun 09, 2024

1. A four-month European put option on a non-dividend-paying stock is currently selling for $2. The stock price is $45, the strike price is $50,

1. A four-month European put option on a non-dividend-paying stock is currently selling for $2. The stock price is $45, the strike price is $50, and the risk-free interest rate is 12% per annum. Is there an arbitrage opportunity? Show the arbitrage transactions now and in four months. (10 marks)

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2. A two-month European call option on a dividend-paying stock is currently selling for $3. The stock price is $55, the strike price is $50, and a dividend of $1.5 is expected in one month. The risk-free interest rate is 12% per annum. Is there an arbitrage opportunity? Show the arbitrage transactions now, in one month and in two months respectively. (15 marks)

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3. A stock price is currently $30. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum. What is the value of a six-month American put option with a strike price of $32? (15 marks)

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4. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $38, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. Value the option using a two-step tree. (15 marks)

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5. Consider the following information:

Time to expiration= 9months

Standard deviation= 25%per year

Exercise price = $35

Stock price = $37

Interest rate = 6% per year

Table for N(x) with selected values

a. Use the Black-Scholes-Merton formula to find the value of a European call option on the stock. [Hint: Use the Cumulative Normal Distribution Table with interpolation.] (10 marks)

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b.Find the value of a European put option with the same exercise price and expiration as the call option above. (5 marks)

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6.Wiley considers a put option that has a delta of -0.35. If the price of the underlying asset decreases by $2, then what is the best estimate of the change in option price? (10 marks)

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7.Brown owns 20,000 shares of CHM. The shares are currently priced at $45. A call option on CHM with a strike price of $50 is selling at $1.50 and has a delta of 0.4. The option contract size is 100 shares. What is the number of call options necessary to create delta-neutral hedge (Buy or write)? (10 marks)

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8.A collar is established by buying a share of stock for $30, buying a six-month put option with exercise price $25, and writing a six-month call option with exercise price $35. Based on the volatility of the stock, you calculate that for an exercise price of $25 and maturity of six months, N(d₁)= 0.65, whereas for the exercise price of $35, N(d₁) = 0.30. What will be the gain or loss on the collar if the stock price increases by $2? (10 marks)

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