FIN5DER Tutorial 11 Problem 12

FIN5DER

Tutorial 11

Problem 12.1.

What is meant by a protective put? What position in call options is equivalent to a protective put?

Problem 12.2.

Explain two ways in which a bear spread can be created.

Problem 12.3.

When is it appropriate for an investor to purchase a butterfly spread?

Problem 12.4.

Call options on a stock are available with strike prices of $15,$17.5 , and $20 and expiration dates in three months. Their prices are $4, $2, and,$0.5 respectively. Explain how the options can be used to create a butterfly spread. Construct a table showing how profit varies with stock price for the butterfly spread.

Problem 12.6.

What is the difference between a strangle and a straddle?

Problem 12.7.

A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from these two options. What is the pattern of profits from the strangle?

Problem 12.8.

Use put–call parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.

Problem 12.9.

Explain how an aggressive bear spread can be created using put options.

Problem 12.10.

Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit and payoff for both spreads.

Problem 12.11.

Use put–call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls.

Problem 12.12.

A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. Construct a table that shows the profit from a straddle. For what range of stock prices would the straddle lead to a loss?

Problem 12.13.

Construct a table showing the payoff from a bull spread when puts with strike prices K₁ and K₂ with K₂ > K₁ are used.

Problem 12.14.

An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction. Identify six different strategies the investor can follow and explain the differences among them.

A Modified Problem 19.20.

Suppose that $70 billion of equity assets are the subject of portfolio insurance schemes. Assume that the schemes are designed to provide insurance against the value of the assets declining by more than 5% within one year. [Making whatever estimates you find necessary, use the DerivaGem software to]

Calculate the value of the stock or futures contracts that the administrators of the portfolio insurance schemes will attempt to sell if the market falls by 23% in a single day. Without using any extra software to estimate the parameters, assume that as

r = 0.06,  s =  0 25 and q = 0.03.

Problem 19.27.

A deposit instrument offered by a bank guarantees that investors will receive a return during a six-month period that is the greater of (a) zero and (b) 40% of the return provided by a market index. An investor is planning to put $100,000 in the instrument. Describe the payoff as an option on the index. Assuming that the risk-free rate of interest is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 25% per annum, is the product a good deal for the investor?