Chapter 16

# Chapter 16 - Option Valuation Our goal in this chapter is...

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16-1 Option Valuation Our goal in this chapter is to discuss stock option prices and its determining factors. We will discuss "implied volatility," which is the market’s forward-looking uncertainty gauge.

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16-2 The Black-Scholes-Merton Option Pricing Model The Black-Scholes option pricing model says the value of a stock option is determined by five factors: S , the current price of the underlying stock. K , the strike price specified in the option contract. r , the risk-free interest rate over the life of the option contract. T , the time remaining until the option contract expires. σ , (sigma) which is the price volatility of the underlying stock.
16-3 The Black-Scholes-Merton Option Pricing Formula The price of a call option on a single share of common stock is: C = SN(d 1 ) – Ke –rT N(d 2 ) The price of a put option on a single share of common stock is: P = Ke –rT N(–d 2 ) – SN(–d 1 ) d 1 and d 2 are calculated using these two formulas: ( 29 ( 29 T σ d d T σ T 2 σ r K S ln d 1 2 2 1 - = + × =

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16-4 Formula Details In the Black-Scholes formula, three common functions are used to price call and put option prices: e -rt , or exp(-rt), is the natural exponent of the value of –rt (in common terms, it is a discount factor) ln(S/K) is the natural log of the "moneyness" term, S/K. N(d1) and N(d2) denotes the standard normal probability for the values of d1 and d2. In addition, the formula makes use of the fact that: N(-d 1 ) = 1 - N(d 1 )
16-5 Varying the Option Price Input Values An important goal of this chapter is to show how an option price changes when only one of the five inputs changes.

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16-6 Varying the Underlying Stock Price
16-7 Varying the Time Remaining Until Option Expiration

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16-8 Varying the Volatility of the Stock Price
16-9 Varying the Interest Rate

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16-10 Calculating Delta Delta measures the dollar impact of a change in the underlying stock price on the value of a stock option.
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