Initial Share price, S 280 Strike Price, K 280 This is an at-the-money put Initial Put Premium, P 2.9701 Initial Futures Price, F 282.8140 Interest rate p.a., r 0.1 Volatility p.a. 0.12 Drift rate for stock 0.15 (ONLY used if you wish to generate a stock price following a GBM) δ ("Dividend" rate) 0 Time to maturity(years) 0.1 (time to maturity of the futures and the options contracts) Timesteps 0.01 V0(stocks) 560000 (Initial dollar value of Stock Portfolio) zf 500 (Futures multiple on stock index futures contract -here $500) M 100 (maturity/face value of T-Bill/bond) HEDGE POSITIONS N0(star) 2000 (Number of stocks in "stock+futures" replication portfolio) N0 1979.007851 (Number of stocks in "stock+put" portfolio) "Delta" Change in Value of … TRUE TRUE Number of Futures Change in Value Change in Delta Stocks Puts Stock + Put Value Change in Futures Price Futures of Stocks Value of Change in value Contracts Price ONLY Stocks Value of Time Time left Asset Delta Delta Call Put ONLY Stock+ Price of Call of Put Option Option Futures Premium Premium t T-t S d1 d2 C P dV(S) dV(P) dV(S+P) V(S+P) dV(S+P) Nf F dF N0(star)xS dV(S+F) 0 0.1 280.0000 0.2825 0.2445 0.6112 -0.3888 5.7561 2.9701 560000 -1.5650579 282.814 560000 0.01 0.1 279.0000 0.1882 0.1503 0.5746 -0.4254 5.1631 3.3771 -1979.008 769.4014 -1209.6065 558826.4 -1173.583 -1.7083761 281.804 -1.0100502 558000 -2000 -1209.6065 0.02 0.1 278.8000 0.1693 0.1314 0.5672 -0.4328 5.0489 3.4629 -395.8016 168.3561 -227.44544 558600.4 -225.9784 -1.7374497 281.602 -0.20201 557600 -400 -227.44544 0.03 0.1 278.5000 0.1409 0.1030 0.5560 -0.4440 4.8804 3.5944 -593.7024 256.9391 -336.7633 558267 -333.4448 -1.781271 281.299 -0.3030151 557000 -600 -336.7633 0.04 0.1 278.0000 0.0936 0.0556 0.5373 -0.4627 4.6071 3.8210 -989.5039 439.2972 -550.20674 557726.1 -540.9243 -1.8547852 280.7939 -0.5050251 556000 -1000 -550.20674 0.05 0.1 277.5000 0.0462 0.0082 0.5184 -0.4816 4.3432 4.0571 -989.5039 457.8604 -531.64348 557203.8 -522.282 -1.9287591 280.2889 -0.5050251 555000 -1000 -531.64348 0.06 0.1 277.0000 -0.0014 -0.0393 0.4995 -0.5005 4.0887 4.3027 -989.5039 476.5398 -512.96413 556700.2 -503.5853 -2.0030292 279.7839 -0.5050251 554000 -1000 -512.96413 0.07 0.1 276.5000 -0.0490 -0.0869 0.4805 -0.5195 3.8437 4.5577 -989.5039 495.2939 -494.21001 556215.4 -484.8506 -2.0774285 279.2789 -0.5050251 553000 -1000 -494.21001 0.08 0.1 276.0000 -0.0967 -0.1346 0.4615 -0.5385 3.6082 4.8222 -989.5039 514.0807 -475.42326 555749.3 -466.0464 -2.1517883 278.7738 -0.5050251 552000 -1000 -475.42326 0.09 0.1 275.5000 -0.1445 -0.1824 0.4426 -0.5574 3.3822 5.0962 -989.5039 532.8574 -456.64648 555302 -447.2809 -2.2259397 278.2688 -0.5050251 551000 -1000 -456.64648 0.1 0.1 275.0000 -0.1923 -0.2303 0.4237 -0.5763 3.1656 5.3796 -989.5039 551.5816 -437.9223 554873.4 -428.5945 -2.2997144 277.7638 -0.5050251 550000 -1000 -437.9223 STOCK + PUT PORTFOLIO STOCK + FUTURES PORTFOLIO Table 13.3 : Portfolio Insurance ('Stock + Futures' Replication Portfolio)Initial Share price, S 280 Strike Price, K 280 Initial Put Premium, P 2.9701 Interest rate p.a., r 0.1 Volatility p.a. 0.12 Drift rate for stock 0.15 δ ("Dividend" rate) 0 Time to maturity 0.1 (years) Timesteps 0.01 V0 (stocks) 560000 Initial dollar value of Stock Portfolio zf 500 Futures multiple on stock index futures contract -here $500 M 100 (maturity/face value of T-Bill/bond) HEDGE POSITIONS N0(star) 2000 (Number of stocks in "stock+futures" replication portfolio) N0 1979.007851 (Number of stocks in "stock+put" portfolio) "Delta" Change in Value of … TRUE TRUE Number Change "Delta" Number Bond Value Stocks Puts Stock + Put Value Change in of stocks in value Change of bonds Price of Bonds Time Time left Asset Delta Delta Call Put value of stocks of stocks+ Price of Call of Put Option Option Bonds Premium Premium t T-t S d1 d2 C P dV(S) dV(P) dV(S+P) V(S+P) dV(S+P) NS NS( dS) dV(S+B) NB B NB x B 0 0.1 280.0000 0.2825 0.2445 0.6112 -0.3888 5.7561 2.9701 560000 1209.606 2235.344 99.00498 221310.1839 0.01 0.1 279.0000 0.1882 0.1503 0.5746 -0.4254 5.1631 3.3771 -1979.008 769.4014 -1209.6065 558826.42 -1173.5826 1137.227 -1209.606 -1209.60649 2439.675 99.00498 241540.0277 0.02 0.1 278.8000 0.1693 0.1314 0.5672 -0.4328 5.0489 3.4629 -395.8016 168.3561 -227.44544 558600.44 -225.97842 1122.544 -227.4454 -227.445441 2481.038 99.00498 245635.0827 0.03 0.1 278.5000 0.1409 0.1030 0.5560 -0.4440 4.8804 3.5944 -593.7024 256.9391 -336.7633 558266.99 -333.44482 1100.413 -336.7633 -336.763296 2543.325 99.00498 251801.8374 0.04 0.1 278.0000 0.0936 0.0556 0.5373 -0.4627 4.6071 3.8210 -989.5039 439.2972 -550.20674 557726.07 -540.9243 1063.287 -550.2067 -550.206745 2647.668 99.00498 262132.2945 0.05 0.1 277.5000 0.0462 0.0082 0.5184 -0.4816 4.3432 4.0571 -989.5039 457.8604 -531.64348 557203.79 -522.28201 1025.928 -531.6435 -531.643481 2752.475 99.00498 272508.6932 0.06 0.1 277.0000 -0.0014 -0.0393 0.4995 -0.5005 4.0887 4.3027 -989.5039 476.5398 -512.96413 556700.2 -503.5853 988.42 -512.9641 -512.964134 2857.511 99.00498 282907.8569 0.07 0.1 276.5000 -0.0490 -0.0869 0.4805 -0.5195 3.8437 4.5577 -989.5039 495.2939 -494.21001 556215.35 -484.85061 950.8465 -494.21 -494.21001 2962.541 99.00498 293306.2888 0.08 0.1 276.0000 -0.0967 -0.1346 0.4615 -0.5385 3.6082 4.8222 -989.5039 514.0807 -475.42326 555749.31 -466.04644 913.293 -475.4233 -475.42326 3067.325 99.00498 303680.451 0.09 0.1 275.5000 -0.1445 -0.1824 0.4426 -0.5574 3.3822 5.0962 -989.5039 532.8574 -456.64648 555302.02 -447.2809 875.8446 -456.6465 -456.646476 3171.627 99.00498 314006.8357 0.1 0.1 275.0000 -0.1923 -0.2303 0.4237 -0.5763 3.1656 5.3796 -989.5039 551.5816 -437.9223 554873.43 -428.59449 838.5866 -437.9223 -437.922303 3275.21 99.00498 324262.1268 Note : the 'delta' change in the STOCK + BOND portfolio is the same as the change in value of the stocks (previous column). Table 13.4 : Portfolio Insurance ('Stock + Bond' Replication Portfolio) STOCK + PUT PORTFOLIO STOCK+BOND PORTFOLIO STOCK+BOND PORTFOLIO