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Unformatted text preview: Chapter 21  Option Valuation CHAPTER 21: OPTION VALUATION Ch21, PS 1 to 6, 8, 11, 12, 19, 2 PROBLEM SETS 1. The value of a put option also increases with the volatility of the stock. We see this from the putcall parity theorem as follows: P = C S + PV(X) + PV(Dividends) Given a value for S and a riskfree interest rate, then, if C increases because of an increase in volatility, P must also increase in order to maintain the equality of the parity relationship. 2. A $1 increase in a call options exercise price would lead to a decrease in the options value of less than $1. The change in the call price would equal $1 only if: (i) there were a 100% probability that the call would be exercised, and (ii) the interest rate were zero. 3. Holding firmspecific risk constant, higher beta implies higher total stock volatility. Therefore, the value of the put option increases as beta increases. 4. Holding beta constant, the stock with a lot of firmspecific risk has higher total volatility. The option on the stock with higher firmspecific risk is worth more. 5. A call option with a high exercise price has a lower hedge ratio. This call option is less in the money. Both d 1 and N(d 1 ) are lower when X is higher. 6. a. Put A must be written on the stock with the lower price. Otherwise, given the lower volatility of Stock A, Put A would sell for less than Put B. b. Put B must be written on the stock with the lower price. This would explain its higher price. c.Call B must have the lower time to expiration. Despite the higher price of Stock B, Call B is cheaper than Call A. This can be explained by a lower time to expiration. d. Call B must be written on the stock with higher volatility. This would explain its higher price. e.Call A must be written on the stock with higher volatility. This would explain its higher price. 211 Chapter 21  Option Valuation 7. Exercise Price Hedge Ratio 120 0/30 = 0.000 110 10/30 = 0.333 100 20/30 = 0.667 90 30/30 = 1.000 As the option becomes more in the money, the hedge ratio increases to a maximum of 1.0. 8. S d 1 N(d 1 ) 450.0268 0.4893 50 0.5000 0.6915 55 0.9766 0.8356 9. a. uS = 130 P u = 0 dS = 80 P d = 30 The hedge ratio is: 5 3 80 130 30 dS uS P P H d u = = = b. Riskless Portfolio S = 80 S = 130 Buy 3 shares 240 390 Buy 5 puts 150 Total 390 390 Present value = $390/1.10 = $354.545 c.The portfolio cost is: 3S + 5P = 300 + 5P The value of the portfolio is: $354.545 Therefore: P = $54.545/5 = $10.91 212 Chapter 21  Option Valuation 10. The hedge ratio for the call is: 5 2 80 130 20 dS uS C C H d u = = = Riskless Portfolio S = 80 S = 130 Buy 2 shares 160 260 Write 5 calls100 Total 160 160 Present value = $160/1.10 = $145.455 The portfolio cost is: 2S 5C = $200 5C The value of the portfolio is: $145.455 Therefore: C = $54.545/5 = $10.91 Does P = C + PV(X) S?...
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This note was uploaded on 12/03/2011 for the course FINS 2624 taught by Professor Hneryyip during the Three '10 term at University of New South Wales.
 Three '10
 HneryYip
 Valuation, Volatility

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