Chapter 21_Hand-out 15

Chapter 21_Hand-out - CHAPTER 21 OPTIONS VALUATION 21.1 OPTION VALUATION INTRODUCTION In the previous chapter we examined option markets and

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CHAPTER 21 OPTIONS VALUATION 21.1 OPTION VALUATION: INTRODUCTION In the previous chapter, we examined option markets and strategies. We ended by noting that many securities contain embedded options that affect both their values and their risk-return characteristics. In this chapter, we turn our attention to option-valuation issues. To understand most option-valuation models requires considerable mathematical and statistical background. Still, many of the ideas and insights of these models can be demonstrated in simple examples, and we will concentrate on these. 1. Intrinsic and Time Values Consider a call option that is out-of-the-money at the moment, with the stock price below the exercise price. This does not mean the option is valueless . Even though immediate exercise today would be unprofitable, the call retains a positive value because there is always a chance the stock price will increase sufficiently by the expiration date to allow for profitable exercise. If not, the worst that can happen is that the option will expire with zero value. The value S 0 — X is sometimes called the intrinsic value of an in-the-money call options because it gives the payoff that could be obtained by immediate exercise. Intrinsic value is set equal to zero for out-of-the-money or at-the- money options. The difference between the actual call price and the intrinsic value is commonly called the time value of the option. (Time value in the options context refers simply to the deference between the option’s price and the value the option would have if it were expiring immediately. It is the part of the option’s value that may be attributed to the fact that it sill has positive time expiration .) Most of an option’s time value typically is a type of " volatility value ." Because the option holder can choose not to exercise, the payoff cannot be worse than zero. Even if a call option is out of the money now, it still will sell for a positive price because it offers the potential for a profit if the stock price increases, while imposing no risk of additional loss should the stock price fall. The volatility value lies in the right not to exercise the call if that action would be unprofitable. The option to exercise as oppose to the obligation to exercise, provides insurance against poor stock price performance. As the stock price increases substantially, it becomes more likely that the call option will be exercised by expiration. Ultimately, with exercise all but assured, the volatility value becomes minimal . As the stock price gets ever larger, the 1
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option value approaches the " adjusted " intrinsic value, that is, the stock price minus the present value of the exercise price, S 0 - PV (X). This discussion presumes the stock pays no dividends until after option expiration. (If the stock does pay dividends, the adjusted intrinsic value of the option must subtract the value of the dividends (D) the stock will pay out before the call is exercised. Adjusted intrinsic value
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This note was uploaded on 09/25/2011 for the course FINA 4320 taught by Professor John during the Spring '11 term at Houston Baptist.

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Chapter 21_Hand-out - CHAPTER 21 OPTIONS VALUATION 21.1 OPTION VALUATION INTRODUCTION In the previous chapter we examined option markets and

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