fm3_chapter21

fm3_chapter21 - UN-14ES56 Stock priceX50 Exercise priceT1...

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Unformatted text preview: UN-14ES56 Stock priceX50 Exercise priceT1 Time remaining r8.00% Risk-free rate of interestSigma30% Stock volatility0.7944 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))0.49440.78650.6895Call price12.22Put price2.38 <-- call price - S + X*Exp(-r*T): by Put-Call parityBlack-Scholes Option Pricing FormulaApplied to General Pills Putd1d2<-- d1-Sigma*SQRT(T)N(d1)<-- Uses formula NormSDist(d1)N(d2)<-- Uses formula NormSDist(d2)<-- S*N(d1)-X*exp(-r*T)*N(d2)ABC123456789101112131415UN-14ES56 Stock priceX50 Exercise priceT1 Time remaining r8.00% Risk-free rate of interestSigma30% Stock volatility0.7944 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))0.49440.78650.6895Call price12.22Put price2.38 <-- call price - S + X*Exp(-r*T): by Put-Call parityCalculating the portfolio insurance proportionsOmega75.45%#MACRO?1-omega24.55%#MACRO?Black-Scholes Option Pricing FormulaApplied to General Pills Putd1d2<-- d1-Sigma*SQRT(T)N(d1)<-- Uses formula NormSDist(d1)N(d2)<-- Uses formula NormSDist(d2)<-- S*N(d1)-X*exp(-r*T)*N(d2)ABC12345678910111213141516171819UN-14ES60 Stock priceX50 Exercise priceT0.9808#MACRO?r8.00% Risk-free rate of interestSigma30% Stock volatility1.0263 <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T))0.72920.84760.7671Call price15.40Put price1.63 <-- call price - S + X*Exp(-r*T): by Put-Call parityCalculating the portfolio insurance proportionsOmega82.53%#MACRO?1-omega17.47%#MACRO?Black-Scholes Option Pricing FormulaApplied to General Pills Putd1d2<-- d1-Sigma*SQRT(T)N(d1)<-- Uses formula NormSDist(d1)N(d2)<-- Uses formula NormSDist(d2)<-- S*N(d1)-X*exp(-r*T)*N(d2)ABC12345678910111213141516171819Pages 581-583Page 4PORTFOLIO INSURANCE SIMULATIONX50 Exercise price of puts in strategy15% Mean of lognormal distribution30% Sigma of lognormal distributionr8% Interest rateInitial1000 Initial investmentPortfolio value, beginning of weekWeekStocksBonds56.0060.000.79440.7545754.50245.501000.00160.0052.001.02630.8253870.06184.221054.27252.00???0.54190.6635622.73315.82938.55Mean, Sigma, Stock priceat begin. ofweekStock priceat end ofweekd1, begining of weekOmega,beginning ofweekPortfoliovaluePages 581-583Page 5Portfolio value, end of weekStocksBonds808.39245.881054.27754.05184.50938.55???316.30???PortfoliovaluePage 585-86Page 6PORTFOLIO INSURANCE SIMULATIONX50 Exercise price of puts in strategy15% Mean of lognormal distribution30% Sigma of lognormal distributionr8% Interest rateInitial1000 Initial investmentPortfolio value, beginWeekStocksBonds56.0053.610.79440.7545754.50245.50153.6150.960.64700.7029680.53287.58250.9650.510.47340.6364595.04339.96350.5147.700.43920.6232579.68350.55447.7047.680.23660.5394484.61413.87547.6845.330.22950.5370482.71416.25645.3346.710.04400.4588401.77474.00746.7148.310.14340.5016445.83442.90848.3149.110.25870.5512498.68406.06949.1148.020.31340.5747525.10388.561048.0245.450.22450.5380485.59416.951145.4547.190.01170.4486393.51483.681247.1947.850.14540.5059451.73441.261347.8548.500.19200.5263473.68426.371448.5044.490.23730.5460495.30411.78411....
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fm3_chapter21 - UN-14ES56 Stock priceX50 Exercise priceT1...

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