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Chapter 5: Q15-17I (page 514)

A bearish spread is the purchase of a call with exercise price X 2 and the sale of a call with exercise price X 1, with X 2 greater than X 1. Graph the payoff to this strategy and compare it to Figure 15.10 .

Short Answer

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As below.

Step by step solution

01

Calculation of bearish period

Position

ST < X1

X1< ST < X2

ST > X2

Long call (x2)

0

0

ST - X2

Short call (x1)

0

(ST - X1)

(ST - X1)

Total

0

X1- ST

X1- X2

02

Payoff diagram of ‘a’

03

Calculation of vertical combination ‘b’

Position

ST < X1

X1< ST < X2

ST > X2

Long call (x2)

0

0

ST - X2

Short call (x1)

X1 - ST

0

0

Total

0

ST - X1

ST - X2

04

Payoff diagram of ‘b’

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Most popular questions from this chapter

The hedge ratio of an at-the-money call option on IBM is .4. The hedge ratio of an at-the-money put option is -6. What is the hedge ratio of an at-the-money straddle position on IBM?

Consider a stock that will pay a dividend of D dollars in one year, which is when a futures contract matures.

Consider the following strategy: Buy the stock, short a futures contract on the stock, and borrow S0dollars, where S0is the current price of the stock.

a. What are the cash flows now and in one year? (Hint: Remember the dividend the stock will pay.)

b. Show that the equilibrium futures price must beF0=S0(1+r)to avoid arbitrage.

c. Call the dividend yield d = D / S0, and conclude that F0=S0(1+r-d).

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a. By how much is the contract mispriced?

b. Formulate a zero-net-investment arbitrage portfolio, and show that you can lock in riskless profits equal to the futures mispricing.

c. Now assume (as is true for small investors) that if you short-sell the stocks in the market index, the proceeds of the short sale are kept with the broker and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming you don’t already own the shares in the index)? Explain.

d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relationship? That is, given a stock index of 1,200, how high and how low can the futures price be without giving rise to arbitrage opportunities?

Suresh Singh, CFA, is analyzing a convertible bond. The characteristics of the bond and the underlying common stock are given in the following exhibit:

Compute the bond’s:

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Show that Black-Scholes call option hedge ratios increase as the stock price increases. Consider a one-year option with exercise price \(50 on a stock with annual standard deviation 20%. The T-bill rate is 3% per year. Find N (d1) for stock prices \)45, \(50, and \)55.
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