## DELTANeutra Positions

Consider a portfolio, P, of a short position of one European call on a nondividend stock combined with a long position of DELTA units of the stock. The portfolio would have the value Continuing to use our sample options of Table 5.6, the cost of the portfolio, assuming a current stock price of 100, would be P -c + N(dt)S - 10.3044 + 0.6151( 100.00) 51.2056 If the stock price were to suddenly change to 100.10, the portfolio's value would be P -c + N(dt)S - 10.3660 + 0.6151( 100.10) 51.2055 Thus,...

## Info

For a DELTA-neutral portfolio comprised of Calls C and D that is long one Call C, we must choose a position of Z shares of Call D to satisfy the following equation Therefore, Z 1.1642, and the portfolio consists of purchasing one Call C and selling 1.1642 units of Call D. To form a portfolio of Calls C, D, and E that is long one Call C and that is also DELTA-neutral and GAMMA-neutral, the portfolio must meet both of the following conditions, where Y and Z are the number of Call Cs and Call Ds,...

## Convertible Bonds

Many corporate bonds are convertible into shares of the issuing firm. The holder of the bond has the option to convert the bond into shares under the terms specified in the bond indenture. For example, a firm might issue a 1,000 face value convertible bond with a 20-year maturity and a coupon rate of 9 percent. The bond could be converted into eight shares of stock by surrendering the bond.3 We assume that a share of the issuing firm was worth 100 at the time of issuance. We can analyze this...

## The Boundary Space For Call And Put Options

In Chapter 2, we saw that the value of a call either European or American at expiration must be Similarly, the value of a put either European or American at expiration is Corresponding to Equations 3.1 and 3.2, we saw that call and put options had distinctive graphs that specified their values at expiration. Figure 2.4 for a call and Figure 2.6 for a put gave the value of the options at expiration. These two figures simply graph Equations 3.1 and 3.2, respectively. Now we want to consider the...

## Review Questions

What is binomial about the binomial model In other words, how does the model get its name 2. If a stock price moves in a manner consistent with the binomial model, what is the chance that the stock price will be the same for two periods in a row Explain. 3. Assume a stock price is 120 and in the next year it will either rise by 10 percent or fall by 20 percent. The risk-free interest rate is 6 percent. A call option on this stock has an exercise price of 130. What is the price of a call...

## Exact American Call Option Pricing

In general, there is no closed-form solution to the value of an American call option on a dividend-paying stock. However, an exact pricing formula is possible in one special case. It is possible to compute the exact price for an option on a stock that pays a single dividend during the life of the option.3 The model is also known as the Compound Option Model. As discussed in the previous section on the pseudo-American model, an American call option really consists of a series of options that...

## Notes

A risk-neutral investor considers only the expected payoffs from an investment. For such an investor, the risk associated with the investment is not important. Thus, a risk-neutral investor would be indifferent between an investment with a certain payoff of 50 or an investment with a 50 percent probability of paying 100 and a 50 percent probability of paying zero. 2. The development of the binomial model stems from two seminal articles R. Rendleman and B. Bartter, Two-State Option Pricing,...

## Introduction

This chapter continues to use no-arbitrage conditions to explore options pricing principles. In the last chapter, we considered the prices options could have at expiration, consistent with no-arbitrage conditions. In this chapter, we consider options prices before expiration. Extending our analysis to options with time remaining until expiration brings new factors into consideration. The value of an option before expiration depends on five factors the price of the underlying stock, the exercise...

## Rho

RHO is the first derivative of an option's price with respect to the interest rate. RHOc is always positive, while RHOp is always negative. In general, options prices are not very sensitive to RHO. In Table 5.6, RHOc 25.2515, and RHOp 22.1559. If the interest rate were to increase by 1 percent, then the call price should increase by 0.01 25.2515 0.2525, while the price of the put should fall by 0.01 22.1559 0.2216. Figure 5.10 shows how the prices of our example options would change given...

## Acknowledgments

The preparation of this book has benefitted from the assistance of a number of people. Andrea Coens provided timely editing and many useful suggestions about the book. Phil Rizika and Adam Carlin reviewed the manuscript and software, and Evelyn Gosnell prepared the graphical illustrations. The students in my futures and options classes in Fall 1993 studied from the pageproofs of this book, giving me a chance to test it in the classroom before publication. A large number of scholars around the...

## Combining Options With Bonds And Stocks

Thus far we have considered some of the most important combinations of options. We now show how to combine options with stocks and bonds to adjust payoff patterns to fit virtually any taste for risk and return combinations. These combinations show us the relationships among the different classes of securities. By combining two types of securities, we Table 2.1 Options Combinations and Their Profits Position Cost Value at Expiration Trader Expects Table 2.1 Options Combinations and Their Profits...

## American And European Options

There are two fundamental kinds of options the American option and the European option. An American option permits the owner to exercise at any time before or at expiration. The owner of a European option can exercise only at expiration. Thus, the two kinds of options differ because the American option permits early exercise. To this point, we have considered option values only at expiration. If the option is at expiration, American and European options will have the same value. Both can be...