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Unformatted text preview: WEEK X Wait (the option to wait) Expand (the option to expand) Exchange  the option to exchange variables Graph of values of the option to exchange More on early exercise of put Riskfree rate rf 0.05 Div Up 10 15 20 25 30 35 40 The Malted Herring project requires an investment of 180 and yields CF with PV=200=S. NPV=200180=20. The project has two possible outcomes: 1. The up state: rate of return (on the market value of 200) = 37.5%, of which 12.5% are cash dividends and 25% capital gains. 2. The down state: rate of return = 12% of which 8% are cash dividends and 20% is capital loss. This worksheet (1) computes the value of the option to wait using the BlackScholes formula and (2) investigates the role of the dividend yield, holding total return constant, in the value of waiting. Taking the up and down states as: u=exp(mean+sigma) = 1.375, d=exp(meansigma) = 0.88. We obtain: mean = 0.0953; sigma = 0.2231. Notice that exp(mean)=1.1 (an effective mean of 10%). Since the project is assumed a perpetuity, this is equal to the dividend rate. The BS value of a stock that pays a discrete dividend in one year (T=1) is: [SPV(Div)]*N(d1) PV(X)*N(d2) where: d1 = ln[ (SPV(Div)) / PV(X) ] / sigma + 0.5*sigma d2= d1 sigma The table shows the value of waiting one year to invest with different levels of dividends. The table shows that a project with the same value but lower dividends is more likely to be postponed than one with higher dividends. Notice that with the same data as in the text (the yellow line), the value of the call is 21.425. The reason is that the onestage binomial tree makes for a different price dynamic of the stock than the BS solution. Breaking up the tree to many stages would yield value of waiting closer to that computed with the BS formula. 0.22 0.22 Possible States RiskNeutral Investment Mkt Value Total return Mean and SD R.N. Prob. I=X PV(X) S u d sigma mean p* 180 171.43 200 1.38 0.88 0.2231 0.0953 0.3434 Value of call with a onestage binomial tree Actual prob Cum Div Div Ex Div Call boundary 0.43 U 275 25 250 70 D 176 16 160 Call value NPV Now 22.90 20 Div Down PV(Div) SPV(Div) d1 d2 N(d1) N(d2) Call value 4 5.77 194.23 0.67 0.4480 0.75 0.67 30.11 8 9.91 190.09 0.57 0.3515 0.72 0.64 27.07 12 14.05 185.95 0.48 0.2529 0.68 0.6 24.18 16 18.18 181.82 0.38 0.1521 0.65 0.56 21.43 20 22.32 177.68 0.27 0.0490 0.61 0.52 18.83 24 26.46 173.54 0.170.0566 0.57 0.48 16.4 28 30.59 169.41 0.060.1647 0.52 0.43 14.15 Using actual probabilities and risky discount rate 18.18 181.82 0.38 0.1521 0.65 0.56 21.43 div rate 0.1 200 0.38 0.1521 0.65 0.56 21.43 Strike...
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This note was uploaded on 05/06/2010 for the course IRPS IRGN 424 taught by Professor Kane during the Fall '09 term at UCSD.
 Fall '09
 Kane

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