I am trying to simulate 2 deals in HON options:1.Sell Call / Buy Put / Long stock --> use call bid price and put ask price2.Buy Call / Sell Put / Short Stock --> use call ask price and put bid priceUsing the following put-call parity equation:C = S - Kexp(-r*t) + PC; call option priceS ; spot rateK : strikeP : put option pricer : mixture of effects of riskfree rate+ dividend yield t : time to maturityImplies=> r = (-1/t)* ln((S+P-C)/K) (Am I wrong??)I tried to find value of r inherent for each of the above deal. eg., In the following table,Date : Maturity date of optionK : strikePA : Put price askCB : call price bidr1 : r obtained by solving put-call parity equation for deal 1 using PA and CBPB : Put price bidCA : call price askr2 : r obtained by solving put-call parity equation for deal 2 using PB and CADate:10/17/2003 K:22.50 PA:0.15 CB: 4.90 r1:-0.59 PB:0.00 CA:5.20 r2:0.22Date:10/17/2003 K:22.50 PA:0.25 CB: 4.80 r1:-0.94 PB:0.00 CA:5.20 r2:0.22Date:10/17/2003 K:22.50 PA:0.10 CB: 4.90 r1:-0.50 PB:0.00 CA:5.30 r2:0.40Date:10/17/2003 K:22.50 PA:0.05 CB: 4.90 r1:-0.41 PB:0.00 CA:5.30 r2:0.40Date:10/17/2003 K:22.50 PA:0.10 CB: 4.90 r1:-0.50 PB:0.00 CA:5.10 r2:0.04Date:10/17/2003 K:25.00 PA:0.15 CB: 2.45 r1:-0.45 PB:0.00 CA:2.75 r2:0.28Date:10/17/2003 K:25.00 PA:0.25 CB: 2.35 r1:-0.77 PB:0.00 CA:2.70 r2:0.20Date:10/17/2003 K:25.00 PA:0.10 CB: 2.40 r1:-0.45 PB:0.00 CA:2.80 r2:0.36Date:10/17/2003 K:25.00 PA:0.10 CB: 2.45 r1:-0.37 PB:0.00 CA:2.80 r2:0.36Date:10/17/2003 K:25.00 PA:0.15 CB: 2.45 r1:-0.45 PB:0.00 CA:2.65 r2:0.11Date:10/17/2003 K:27.50 PA:0.55 CB: 0.45 r1:-0.26 PB:0.50 CA:0.60 r2:0.03Date:10/17/2003 K:27.50 PA:0.65 CB: 0.40 r1:-0.48 PB:0.40 CA:0.65 r2:0.25Date:10/17/2003 K:27.50 PA:0.60 CB: 0.45 r1:-0.34 PB:0.35 CA:0.65 r2:0.33Date:10/17/2003 K:27.50 PA:0.55 CB: 0.50 r1:-0.19 PB:0.50 CA:0.55 r2:-0.04Date:10/17/2003 K:27.50 PA:0.60 CB: 0.50 r1:-0.26 PB:0.45 CA:0.60 r2:0.10Date:10/17/2003 K:30.00 PA:2.60 CB: 0.00 r1:-0.24 PB:2.30 CA:0.05 r2:0.23Date:10/17/2003 K:30.00 PA:2.65 CB: 0.00 r1:-0.31 PB:2.30 CA:0.25 r2:0.50Date:10/17/2003 K:30.00 PA:2.65 CB: 0.00 r1:-0.31 PB:2.25 CA:0.10 r2:0.37Date:10/17/2003 K:30.00 PA:2.60 CB: 0.00 r1:-0.24 PB:2.25 CA:0.10 r2:0.37Date:10/17/2003 K:30.00 PA:2.60 CB: 0.00 r1:-0.24 PB:2.40 CA:0.10 r2:0.16Date:10/17/2003 K:32.50 PA:5.10 CB: 0.00 r1:-0.22 PB:4.80 CA:0.15 r2:0.34Date:10/17/2003 K:32.50 PA:5.20 CB: 0.00 r1:-0.35 PB:4.80 CA:0.25 r2:0.46Date:10/17/2003 K:32.50 PA:5.10 CB: 0.00 r1:-0.22 PB:4.70 CA:0.10 r2:0.40Date:10/17/2003 K:32.50 PA:5.10 CB: 0.00 r1:-0.22 PB:4.70 CA:0.05 r2:0.34Date:10/17/2003 K:32.50 PA:5.10 CB: 0.00 r1:-0.22 PB:4.90 CA:0.10 r2:0.15Date:11/21/2003 K:22.50 PA:0.15 CB: 5.00 r1:-0.08 PB:0.00 CA:5.30 r2:0.08Date:11/21/2003 K:22.50 PA:0.25 CB: 4.90 r1:-0.16 PB:0.00 CA:5.30 r2:0.08Date:11/21/2003 K:22.50 PA:0.15 CB: 4.90 r1:-0.12 PB:0.00 CA:5.30 r2:0.08Date:11/21/2003 K:22.50 PA:0.15 CB: 5.00 r1:-0.08 PB:0.00 CA:5.30 r2:0.08Date:11/21/2003 K:22.50 PA:0.15 CB: 5.00 r1:-0.08 PB:0.00 CA:5.20 r2:0.04Date:11/21/2003 K:25.00 PA:0.40 CB: 2.70 r1:-0.09 PB:0.25 CA:3.00 r2:0.06Date:11/21/2003 K:25.00 PA:0.45 CB: 2.65 r1:-0.13 PB:0.20 CA:3.00 r2:0.07Date:11/21/2003 K:25.00 PA:0.40 CB: 2.70 r1:-0.09 PB:0.25 CA:2.95 r2:0.04Date:11/21/2003 K:25.00 PA:0.35 CB: 2.65 r1:-0.09 PB:0.25 CA:3.00 r2:0.06Date:11/21/2003 K:25.00 PA:0.40 CB: 2.70 r1:-0.09 PB:0.25 CA:2.90 r2:0.02Date:11/21/2003 K:27.50 PA:1.15 CB: 0.95 r1:-0.08 PB:1.00 CA:1.10 r2:0.01Date:11/21/2003 K:27.50 PA:1.30 CB: 1.00 r1:-0.11 PB:1.05 CA:1.25 r2:0.04Date:11/21/2003 K:27.50 PA:1.20 CB: 0.95 r1:-0.10 PB:1.00 CA:1.15 r2:0.02Date:11/21/2003 K:27.50 PA:1.15 CB: 1.00 r1:-0.07 PB:1.00 CA:1.10 r2:0.01Date:11/21/2003 K:27.50 PA:1.20 CB: 0.95 r1:-0.10 PB:1.05 CA:1.15 r2:0.01Date:11/21/2003 K:30.00 PA:2.95 CB: 0.15 r1:-0.10 PB:2.65 CA:0.30 r2:0.02Date:11/21/2003 K:30.00 PA:3.10 CB: 0.15 r1:-0.15 PB:2.75 CA:0.35 r2:0.01Date:11/21/2003 K:30.00 PA:2.90 CB: 0.10 r1:-0.10 PB:2.65 CA:0.30 r2:0.02Date:11/21/2003 K:30.00 PA:2.95 CB: 0.15 r1:-0.10 PB:2.60 CA:0.25 r2:0.02Date:11/21/2003 K:30.00 PA:2.95 CB: 0.15 r1:-0.10 PB:2.75 CA:0.25 r2:-0.02Date:11/21/2003 K:32.50 PA:5.30 CB: 0.00 r1:-0.10 PB:5.00 CA:0.15 r2:0.02Date:11/21/2003 K:32.50 PA:5.40 CB: 0.00 r1:-0.12 PB:5.00 CA:0.25 r2:0.04Date:11/21/2003 K:32.50 PA:5.30 CB: 0.00 r1:-0.10 PB:4.90 CA:0.10 r2:0.03Date:11/21/2003 K:32.50 PA:5.30 CB: 0.00 r1:-0.10 PB:4.90 CA:0.10 r2:0.03Date:11/21/2003 K:32.50 PA:5.30 CB: 0.00 r1:-0.10 PB:5.00 CA:0.10 r2:0.01Date:12/19/2003 K:17.50 PA:0.15 CB: 9.90 r1:-0.09 PB:0.00 CA:10.30 r2:0.06Date:12/19/2003 K:17.50 PA:0.25 CB: 9.80 r1:-0.15 PB:0.00 CA:10.30 r2:0.06Date:12/19/2003 K:17.50 PA:0.10 CB: 9.80 r1:-0.11 PB:0.00 CA:10.30 r2:0.06Date:12/19/2003 K:17.50 PA:0.10 CB: 9.90 r1:-0.08 PB:0.05 CA:10.30 r2:0.05Date:12/19/2003 K:17.50 PA:0.10 CB: 9.90 r1:-0.08 PB:0.00 CA:10.10 r2:0.01Date:12/19/2003 K:20.00 PA:0.15 CB: 7.40 r1:-0.08 PB:0.00 CA:7.80 r2:0.06Date:12/19/2003 K:20.00 PA:0.25 CB: 7.30 r1:-0.13 PB:0.00 CA:7.80 r2:0.06Date:12/19/2003 K:20.00 PA:0.10 CB: 7.30 r1:-0.10 PB:0.00 CA:7.80 r2:0.06Date:12/19/2003 K:20.00 PA:0.10 CB: 7.40 r1:-0.07 PB:0.00 CA:7.80 r2:0.06Date:12/19/2003 K:20.00 PA:0.10 CB: 7.50 r1:-0.05 PB:0.00 CA:7.70 r2:0.03Date:12/19/2003 K:22.50 PA:0.25 CB: 5.10 r1:-0.05 PB:0.10 CA:5.50 r2:0.07Date:12/19/2003 K:22.50 PA:0.30 CB: 5.00 r1:-0.08 PB:0.05 CA:5.40 r2:0.06Date:12/19/2003 K:22.50 PA:0.25 CB: 5.00 r1:-0.07 PB:0.10 CA:5.40 r2:0.05Date:12/19/2003 K:22.50 PA:0.25 CB: 5.00 r1:-0.07 PB:0.10 CA:5.40 r2:0.05Date:12/19/2003 K:22.50 PA:0.25 CB: 5.10 r1:-0.05 PB:0.10 CA:5.20 r2:0.00Date:12/19/2003 K:25.00 PA:0.65 CB: 2.90 r1:-0.07 PB:0.50 CA:3.20 r2:0.02Date:12/19/2003 K:25.00 PA:0.70 CB: 2.85 r1:-0.09 PB:0.45 CA:3.20 r2:0.03Date:12/19/2003 K:25.00 PA:0.65 CB: 2.85 r1:-0.08 PB:0.45 CA:3.20 r2:0.03Date:12/19/2003 K:25.00 PA:0.60 CB: 2.85 r1:-0.07 PB:0.45 CA:3.20 r2:0.03Date:12/19/2003 K:25.00 PA:0.60 CB: 2.90 r1:-0.06 PB:0.45 CA:3.10 r2:0.01Date:12/19/2003 K:27.50 PA:1.50 CB: 1.25 r1:-0.06 PB:1.35 CA:1.40 r2:-0.01Date:12/19/2003 K:27.50 PA:1.60 CB: 1.25 r1:-0.08 PB:1.35 CA:1.50 r2:0.01Date:12/19/2003 K:27.50 PA:1.55 CB: 1.25 r1:-0.07 PB:1.30 CA:1.45 r2:0.01Date:12/19/2003 K:27.50 PA:1.45 CB: 1.25 r1:-0.05 PB:1.30 CA:1.40 r2:0.00Date:12/19/2003 K:27.50 PA:1.50 CB: 1.25 r1:-0.06 PB:1.35 CA:1.35 r2:-0.01Date:12/19/2003 K:30.00 PA:3.20 CB: 0.40 r1:-0.06 PB:2.90 CA:0.55 r2:0.01Date:12/19/2003 K:30.00 PA:3.30 CB: 0.35 r1:-0.09 PB:2.95 CA:0.60 r2:0.01Date:12/19/2003 K:30.00 PA:3.20 CB: 0.30 r1:-0.08 PB:2.85 CA:0.50 r2:0.01Date:12/19/2003 K:30.00 PA:3.20 CB: 0.35 r1:-0.07 PB:2.85 CA:0.50 r2:0.01Date:12/19/2003 K:30.00 PA:3.10 CB: 0.35 r1:-0.06 PB:2.95 CA:0.50 r2:-0.01Date:12/19/2003 K:32.50 PA:5.30 CB: 0.10 r1:-0.04 PB:5.00 CA:0.15 r2:0.01Date:12/19/2003 K:32.50 PA:5.40 CB: 0.00 r1:-0.07 PB:5.00 CA:0.25 r2:0.03Date:12/19/2003 K:32.50 PA:5.40 CB: 0.05 r1:-0.07 PB:5.00 CA:0.15 r2:0.01Date:12/19/2003 K:32.50 PA:5.40 CB: 0.05 r1:-0.07 PB:5.00 CA:0.20 r2:0.02Date:12/19/2003 K:32.50 PA:5.30 CB: 0.05 r1:-0.05 PB:5.10 CA:0.15 r2:-0.00Date:01/16/2004 K:10.00 PA:0.15 CB: 17.30 r1:-0.15 PB:0.00 CA:17.90 r2:0.12Date:01/16/2004 K:10.00 PA:0.25 CB: 17.10 r1:-0.26 PB:0.00 CA:17.90 r2:0.12Date:01/16/2004 K:10.00 PA:0.05 CB: 17.20 r1:-0.15 PB:0.00 CA:18.00 r2:0.16Date:01/16/2004 K:10.00 PA:0.05 CB: 17.40 r1:-0.08 PB:0.00 CA:17.80 r2:0.08Date:01/16/2004 K:10.00 PA:0.05 CB: 17.40 r1:-0.08 PB:0.00 CA:17.60 r2:0.01Date:01/16/2004 K:15.00 PA:0.15 CB: 12.30 r1:-0.10 PB:0.00 CA:12.90 r2:0.08Date:01/16/2004 K:15.00 PA:0.25 CB: 12.20 r1:-0.15 PB:0.00 CA:12.90 r2:0.08Date:01/16/2004 K:15.00 PA:0.10 CB: 12.20 r1:-0.11 PB:0.00 CA:13.00 r2:0.10Date:01/16/2004 K:15.00 PA:0.05 CB: 12.40 r1:-0.06 PB:0.00 CA:12.80 r2:0.05Date:01/16/2004 K:15.00 PA:0.10 CB: 12.40 r1:-0.07 PB:0.00 CA:12.60 r2:0.00Date:01/16/2004 K:20.00 PA:0.20 CB: 7.40 r1:-0.07 PB:0.05 CA:7.80 r2:0.03Date:01/16/2004 K:20.00 PA:0.25 CB: 7.30 r1:-0.10 PB:0.00 CA:7.80 r2:0.04Date:01/16/2004 K:20.00 PA:0.25 CB: 7.40 r1:-0.08 PB:0.05 CA:7.90 r2:0.05Date:01/16/2004 K:20.00 PA:0.15 CB: 7.50 r1:-0.04 PB:0.10 CA:7.80 r2:0.02Date:01/16/2004 K:20.00 PA:0.15 CB: 7.50 r1:-0.04 PB:0.05 CA:7.70 r2:0.01Date:01/16/2004 K:25.00 PA:0.80 CB: 3.00 r1:-0.06 PB:0.65 CA:3.30 r2:0.01Date:01/16/2004 K:25.00 PA:0.85 CB: 2.90 r1:-0.08 PB:0.60 CA:3.30 r2:0.02Date:01/16/2004 K:25.00 PA:0.85 CB: 3.10 r1:-0.05 PB:0.65 CA:3.40 r2:0.02Date:01/16/2004 K:25.00 PA:0.75 CB: 3.00 r1:-0.05 PB:0.65 CA:3.40 r2:0.02Date:01/16/2004 K:25.00 PA:0.80 CB: 3.00 r1:-0.06 PB:0.65 CA:3.20 r2:-0.00Date:01/16/2004 K:27.50 PA:1.70 CB: 1.55 r1:-0.03 PB:1.55 CA:1.65 r2:0.00Date:01/16/2004 K:27.50 PA:1.85 CB: 1.50 r1:-0.06 PB:1.60 CA:1.75 r2:0.01Date:01/16/2004 K:27.50 PA:1.75 CB: 1.50 r1:-0.04 PB:1.55 CA:1.70 r2:0.01Date:01/16/2004 K:27.50 PA:1.70 CB: 1.50 r1:-0.04 PB:1.55 CA:1.65 r2:0.00Date:01/16/2004 K:27.50 PA:1.70 CB: 1.45 r1:-0.04 PB:1.55 CA:1.60 r2:-0.00Date:01/16/2004 K:30.00 PA:3.40 CB: 0.60 r1:-0.05 PB:3.10 CA:0.65 r2:-0.00Date:01/16/2004 K:30.00 PA:3.50 CB: 0.55 r1:-0.06 PB:3.10 CA:0.65 r2:-0.00Date:01/16/2004 K:30.00 PA:3.40 CB: 0.55 r1:-0.05 PB:3.00 CA:0.80 r2:0.03Date:01/16/2004 K:30.00 PA:3.40 CB: 0.60 r1:-0.05 PB:3.00 CA:0.70 r2:0.01Date:01/16/2004 K:30.00 PA:3.30 CB: 0.55 r1:-0.04 PB:3.10 CA:0.70 r2:0.00Date:01/16/2004 K:35.00 PA:7.80 CB: 0.05 r1:-0.03 PB:7.40 CA:0.15 r2:0.02Date:01/16/2004 K:35.00 PA:7.90 CB: 0.00 r1:-0.05 PB:7.40 CA:0.25 r2:0.03Date:01/16/2004 K:35.00 PA:7.90 CB: 0.05 r1:-0.04 PB:7.40 CA:0.20 r2:0.02Date:01/16/2004 K:35.00 PA:7.80 CB: 0.05 r1:-0.03 PB:7.40 CA:0.15 r2:0.02Date:01/16/2004 K:35.00 PA:7.80 CB: 0.05 r1:-0.03 PB:7.60 CA:0.15 r2:-0.00Date:01/16/2004 K:40.00 PA:12.80 CB: 0.00 r1:-0.03 PB:12.20 CA:0.15 r2:0.03Date:01/16/2004 K:40.00 PA:13.00 CB: 0.00 r1:-0.05 PB:12.30 CA:0.25 r2:0.03Date:01/16/2004 K:40.00 PA:13.00 CB: 0.00 r1:-0.05 PB:12.20 CA:0.15 r2:0.03Date:01/16/2004 K:40.00 PA:12.80 CB: 0.00 r1:-0.03 PB:12.40 CA:0.10 r2:0.01Date:01/16/2004 K:40.00 PA:12.70 CB: 0.00 r1:-0.03 PB:12.50 CA:0.10 r2:0.00Date:01/16/2004 K:45.00 PA:0.00 CB: 0.00 r1:1.79 PB:0.00 CA:0.00 r2:1.79Date:01/16/2004 K:50.00 PA:22.90 CB: 0.00 r1:-0.03 PB:22.10 CA:0.15 r2:0.03Date:01/16/2004 K:50.00 PA:23.10 CB: 0.00 r1:-0.05 PB:22.10 CA:0.25 r2:0.04Date:01/16/2004 K:50.00 PA:23.10 CB: 0.00 r1:-0.05 PB:22.10 CA:0.10 r2:0.03Date:01/16/2004 K:50.00 PA:22.70 CB: 0.00 r1:-0.02 PB:22.40 CA:0.05 r2:0.01Date:01/16/2004 K:50.00 PA:22.70 CB: 0.00 r1:-0.02 PB:22.50 CA:0.10 r2:0.00Date:01/16/2004 K:60.00 PA:32.90 CB: 0.00 r1:-0.03 PB:32.10 CA:0.15 r2:0.03Date:01/16/2004 K:60.00 PA:33.10 CB: 0.00 r1:-0.04 PB:32.10 CA:0.25 r2:0.03Date:01/16/2004 K:60.00 PA:33.00 CB: 0.00 r1:-0.04 PB:32.00 CA:0.10 r2:0.03Date:01/16/2004 K:60.00 PA:32.70 CB: 0.00 r1:-0.02 PB:32.40 CA:0.05 r2:0.00Date:01/16/2004 K:60.00 PA:32.70 CB: 0.00 r1:-0.02 PB:32.50 CA:0.10 r2:0.00Date:03/19/2004 K:22.50 PA:0.65 CB: 5.30 r1:-0.04 PB:0.50 CA:5.70 r2:0.01Date:03/19/2004 K:22.50 PA:0.70 CB: 5.20 r1:-0.06 PB:0.45 CA:5.70 r2:0.02Date:03/19/2004 K:22.50 PA:0.65 CB: 5.20 r1:-0.05 PB:0.45 CA:5.70 r2:0.02Date:03/19/2004 K:22.50 PA:0.65 CB: 5.30 r1:-0.04 PB:0.45 CA:5.60 r2:0.01Date:03/19/2004 K:22.50 PA:0.65 CB: 5.30 r1:-0.04 PB:0.50 CA:5.50 r2:-0.01Date:03/19/2004 K:25.00 PA:1.20 CB: 3.40 r1:-0.03 PB:1.05 CA:3.70 r2:0.01Date:03/19/2004 K:25.00 PA:1.25 CB: 3.30 r1:-0.05 PB:1.00 CA:3.70 r2:0.01Date:03/19/2004 K:25.00 PA:1.25 CB: 3.30 r1:-0.05 PB:1.05 CA:3.70 r2:0.01Date:03/19/2004 K:25.00 PA:1.25 CB: 3.30 r1:-0.05 PB:1.05 CA:3.70 r2:0.01Date:03/19/2004 K:25.00 PA:1.25 CB: 3.40 r1:-0.04 PB:1.05 CA:3.60 r2:-0.00Date:03/19/2004 K:27.50 PA:2.25 CB: 1.90 r1:-0.03 PB:2.00 CA:2.05 r2:-0.00Date:03/19/2004 K:27.50 PA:2.35 CB: 1.90 r1:-0.04 PB:2.00 CA:2.15 r2:0.01Date:03/19/2004 K:27.50 PA:2.25 CB: 1.85 r1:-0.04 PB:2.00 CA:2.10 r2:0.00Date:03/19/2004 K:27.50 PA:2.25 CB: 1.90 r1:-0.03 PB:2.05 CA:2.10 r2:-0.00Date:03/19/2004 K:27.50 PA:2.25 CB: 1.85 r1:-0.04 PB:2.05 CA:2.05 r2:-0.01Date:03/19/2004 K:30.00 PA:3.80 CB: 0.90 r1:-0.04 PB:3.50 CA:1.00 r2:-0.01Date:03/19/2004 K:30.00 PA:3.90 CB: 0.85 r1:-0.05 PB:3.50 CA:1.10 r2:0.00Date:03/19/2004 K:30.00 PA:3.80 CB: 0.85 r1:-0.04 PB:3.50 CA:1.10 r2:0.00Date:03/19/2004 K:30.00 PA:3.80 CB: 0.90 r1:-0.04 PB:3.50 CA:1.10 r2:0.00Date:03/19/2004 K:30.00 PA:3.80 CB: 0.90 r1:-0.04 PB:3.60 CA:1.00 r2:-0.01Date:03/19/2004 K:32.50 PA:5.80 CB: 0.40 r1:-0.03 PB:5.40 CA:0.50 r2:0.00Date:03/19/2004 K:32.50 PA:5.90 CB: 0.30 r1:-0.05 PB:5.40 CA:0.55 r2:0.00Date:03/19/2004 K:32.50 PA:5.80 CB: 0.35 r1:-0.04 PB:5.40 CA:0.55 r2:0.00Date:03/19/2004 K:32.50 PA:5.80 CB: 0.35 r1:-0.04 PB:5.40 CA:0.50 r2:0.00Date:03/19/2004 K:32.50 PA:5.80 CB: 0.35 r1:-0.04 PB:5.50 CA:0.50 r2:-0.01Date:01/21/2005 K:5.00 PA:0.35 CB: 21.80 r1:-0.16 PB:0.00 CA:23.30 r2:0.12Date:01/21/2005 K:5.00 PA:0.25 CB: 22.00 r1:-0.12 PB:0.00 CA:23.00 r2:0.07Date:01/21/2005 K:5.00 PA:0.10 CB: 22.10 r1:-0.09 PB:0.00 CA:23.10 r2:0.09Date:01/21/2005 K:5.00 PA:0.10 CB: 22.40 r1:-0.04 PB:0.00 CA:22.80 r2:0.03Date:01/21/2005 K:5.00 PA:0.10 CB: 22.40 r1:-0.04 PB:0.00 CA:22.60 r2:0.00Date:01/21/2005 K:10.00 PA:0.35 CB: 17.00 r1:-0.07 PB:0.00 CA:18.20 r2:0.05Date:01/21/2005 K:10.00 PA:0.25 CB: 17.20 r1:-0.05 PB:0.00 CA:17.90 r2:0.03Date:01/21/2005 K:10.00 PA:0.20 CB: 17.20 r1:-0.04 PB:0.00 CA:18.00 r2:0.03Date:01/21/2005 K:10.00 PA:0.15 CB: 17.40 r1:-0.03 PB:0.00 CA:17.80 r2:0.02Date:01/21/2005 K:10.00 PA:0.15 CB: 17.40 r1:-0.03 PB:0.05 CA:17.60 r2:-0.00Date:01/21/2005 K:15.00 PA:0.45 CB: 12.00 r1:-0.05 PB:0.10 CA:13.20 r2:0.03Date:01/21/2005 K:15.00 PA:0.50 CB: 12.30 r1:-0.04 PB:0.25 CA:12.90 r2:0.00Date:01/21/2005 K:15.00 PA:0.45 CB: 12.20 r1:-0.04 PB:0.25 CA:13.00 r2:0.01Date:01/21/2005 K:15.00 PA:0.40 CB: 12.40 r1:-0.03 PB:0.25 CA:12.80 r2:-0.00Date:01/21/2005 K:15.00 PA:0.45 CB: 12.50 r1:-0.03 PB:0.30 CA:12.70 r2:-0.01Date:01/21/2005 K:20.00 PA:1.15 CB: 7.80 r1:-0.04 PB:0.80 CA:8.50 r2:0.00Date:01/21/2005 K:20.00 PA:1.25 CB: 8.00 r1:-0.03 PB:1.00 CA:8.50 r2:-0.00Date:01/21/2005 K:20.00 PA:1.15 CB: 7.90 r1:-0.03 PB:0.90 CA:8.40 r2:-0.00Date:01/21/2005 K:20.00 PA:1.15 CB: 7.90 r1:-0.03 PB:0.95 CA:8.40 r2:-0.01Date:01/21/2005 K:20.00 PA:1.15 CB: 8.00 r1:-0.03 PB:0.95 CA:8.30 r2:-0.01Date:01/21/2005 K:25.00 PA:2.85 CB: 4.40 r1:-0.03 PB:2.25 CA:5.00 r2:0.01Date:01/21/2005 K:25.00 PA:2.85 CB: 4.50 r1:-0.03 PB:2.50 CA:4.90 r2:-0.01Date:01/21/2005 K:25.00 PA:2.65 CB: 4.40 r1:-0.03 PB:2.40 CA:4.80 r2:-0.01Date:01/21/2005 K:25.00 PA:2.70 CB: 4.40 r1:-0.03 PB:2.45 CA:4.90 r2:-0.00Date:01/21/2005 K:25.00 PA:2.65 CB: 4.50 r1:-0.02 PB:2.40 CA:4.70 r2:-0.01Date:01/21/2005 K:30.00 PA:5.40 CB: 2.05 r1:-0.02 PB:4.80 CA:2.65 r2:0.01Date:01/21/2005 K:30.00 PA:5.60 CB: 2.20 r1:-0.02 PB:5.10 CA:2.55 r2:-0.00Date:01/21/2005 K:30.00 PA:5.30 CB: 2.10 r1:-0.02 PB:4.90 CA:2.40 r2:-0.00Date:01/21/2005 K:30.00 PA:5.40 CB: 2.15 r1:-0.02 PB:5.10 CA:2.25 r2:-0.01Date:01/21/2005 K:30.00 PA:5.30 CB: 2.10 r1:-0.02 PB:5.10 CA:2.35 r2:-0.01Date:01/21/2005 K:35.00 PA:9.20 CB: 0.85 r1:-0.02 PB:8.40 CA:1.20 r2:0.00Date:01/21/2005 K:35.00 PA:9.20 CB: 0.90 r1:-0.02 PB:8.70 CA:1.15 r2:-0.00Date:01/21/2005 K:35.00 PA:9.00 CB: 0.85 r1:-0.02 PB:8.60 CA:1.10 r2:-0.00Date:01/21/2005 K:35.00 PA:9.10 CB: 0.90 r1:-0.02 PB:8.70 CA:1.20 r2:-0.00Date:01/21/2005 K:35.00 PA:9.00 CB: 0.90 r1:-0.01 PB:8.70 CA:1.10 r2:-0.00Date:01/21/2005 K:40.00 PA:13.70 CB: 0.30 r1:-0.02 PB:12.50 CA:0.60 r2:0.01Date:01/21/2005 K:40.00 PA:13.60 CB: 0.30 r1:-0.02 PB:13.00 CA:0.55 r2:-0.00Date:01/21/2005 K:40.00 PA:13.50 CB: 0.30 r1:-0.01 PB:12.70 CA:0.50 r2:0.00Date:01/21/2005 K:40.00 PA:13.40 CB: 0.35 r1:-0.01 PB:13.00 CA:0.55 r2:-0.00Date:01/21/2005 K:40.00 PA:13.30 CB: 0.30 r1:-0.01 PB:13.10 CA:0.45 r2:-0.00Date:01/21/2005 K:45.00 PA:18.40 CB: 0.05 r1:-0.02 PB:17.20 CA:0.40 r2:0.01Date:01/21/2005 K:45.00 PA:18.30 CB: 0.00 r1:-0.02 PB:17.60 CA:0.25 r2:0.00Date:01/21/2005 K:45.00 PA:18.20 CB: 0.05 r1:-0.01 PB:17.40 CA:0.25 r2:0.00Date:01/21/2005 K:45.00 PA:18.10 CB: 0.10 r1:-0.01 PB:17.70 CA:0.30 r2:0.00Date:01/21/2005 K:45.00 PA:18.00 CB: 0.10 r1:-0.01 PB:17.80 CA:0.25 r2:-0.00Date:01/20/2006 K:20.00 PA:2.00 CB: 8.50 r1:-0.02 PB:1.65 CA:9.30 r2:0.00Date:01/20/2006 K:20.00 PA:2.10 CB: 8.50 r1:-0.03 PB:1.70 CA:9.30 r2:0.00Date:01/20/2006 K:20.00 PA:2.10 CB: 8.50 r1:-0.03 PB:1.75 CA:9.00 r2:-0.01Date:01/20/2006 K:20.00 PA:2.15 CB: 8.30 r1:-0.03 PB:1.65 CA:9.30 r2:0.00Date:01/20/2006 K:20.00 PA:2.00 CB: 8.70 r1:-0.02 PB:1.85 CA:8.90 r2:-0.01Date:01/20/2006 K:25.00 PA:3.90 CB: 5.40 r1:-0.02 PB:3.30 CA:6.20 r2:0.01Date:01/20/2006 K:25.00 PA:4.00 CB: 5.50 r1:-0.02 PB:3.30 CA:6.10 r2:0.00Date:01/20/2006 K:25.00 PA:4.00 CB: 5.40 r1:-0.02 PB:3.50 CA:5.90 r2:-0.00Date:01/20/2006 K:25.00 PA:4.10 CB: 5.20 r1:-0.03 PB:3.30 CA:6.20 r2:0.01Date:01/20/2006 K:25.00 PA:3.90 CB: 5.50 r1:-0.02 PB:3.60 CA:5.80 r2:-0.01Date:01/20/2006 K:30.00 PA:6.60 CB: 3.20 r1:-0.01 PB:5.80 CA:3.80 r2:0.01Date:01/20/2006 K:30.00 PA:7.00 CB: 3.40 r1:-0.02 PB:6.20 CA:4.10 r2:0.00Date:01/20/2006 K:30.00 PA:6.70 CB: 3.20 r1:-0.02 PB:6.10 CA:3.70 r2:0.00Date:01/20/2006 K:30.00 PA:6.80 CB: 3.10 r1:-0.02 PB:5.80 CA:3.90 r2:0.01Date:01/20/2006 K:30.00 PA:6.50 CB: 3.20 r1:-0.01 PB:6.20 CA:3.60 r2:-0.00Date:01/20/2006 K:35.00 PA:10.00 CB: 2.00 r1:-0.01 PB:9.20 CA:2.50 r2:0.01Date:01/20/2006 K:35.00 PA:10.20 CB: 1.90 r1:-0.01 PB:9.40 CA:2.30 r2:0.00Date:01/20/2006 K:35.00 PA:10.10 CB: 1.80 r1:-0.01 PB:9.50 CA:2.25 r2:0.00Date:01/20/2006 K:35.00 PA:10.20 CB: 1.80 r1:-0.01 PB:9.20 CA:2.30 r2:0.01Date:01/20/2006 K:35.00 PA:9.90 CB: 1.80 r1:-0.01 PB:9.50 CA:2.05 r2:-0.00Date:01/20/2006 K:40.00 PA:14.20 CB: 1.00 r1:-0.01 PB:13.00 CA:1.35 r2:0.01Date:01/20/2006 K:40.00 PA:14.40 CB: 1.10 r1:-0.01 PB:13.40 CA:1.50 r2:0.01Date:01/20/2006 K:40.00 PA:14.10 CB: 1.00 r1:-0.01 PB:13.30 CA:1.35 r2:0.01Date:01/20/2006 K:40.00 PA:14.40 CB: 0.90 r1:-0.01 PB:12.80 CA:1.40 r2:0.01Date:01/20/2006 K:40.00 PA:13.90 CB: 1.00 r1:-0.01 PB:13.50 CA:1.15 r2:0.00On analyzing r1 and r2 , I noted the following observations:1. Both r1 and r2 are at high levels in the beginning , and approach near 0 till 2006.(does it imply that dividend is not expected around 2006?)2. r1 and r2 seem to be same but of oppposite signs at most of the points.Could someone please explain the reason for the trend?Also, why is r2 dropped a large amount from 10/17/2003 to 11/21/2003? The dividend details for HON are as follows, but they don't seem to effect it( am I wrong??):Dividends & Splits Annual Dividend: 0.75 Dividend Yield: 2.58% Dividend Date: 10-Sep-03 Ex-Dividend Date: 18-Aug-03 Last Split Factor (new per old)²: 2:1 Last Split Date: 16-Sep-97 When r2 is highly positive and the maturity is not beyond the coming month of Aug(dividend date), is it and arbitrage to go for the deal?Thanks,asd

I can see you are finally taking my advice and looking at your rates.Now, looking quickly at the data, what you are doing is correct, it seems. However, I don't have enough info to verify your calculations.To use the Call-Put-Parity, it is actually more consistent to use the implied forward price from the option:The equation becomes C =(F-K)*exp(-r*T)+P. Solving for F via iteration (i.e. find the point K where C-P is exactly 0, that is your implied forward price)Then use F in the equation and solve for all R's. Order them in ascending order. Take the median value. Not the average, as you are bound to have some huge outliers.This has the advantage of doing away with having to consider costs of carry effects, like equity lending/equity repo. I assume that's what's causing your distortions.Hope this helps.

I'm also delighted to see that you're looking properly at the forward rates. Let me suggest an alternative to FDAX's method. I'm pretty sure that this way is equivalent to the FDAX approach.1. Start with put-call parity:Share + Put = Bond + CallS + P = K.exp(-r.t) + C2. Write down an expression for the price of a forward:F = S.exp((r-d).t)Where d represents the total of dividend yield, dividend tax and stock borrow costs.3. Put these two expressions together:F.exp((d-r).t) + P = K.exp(-r.t) + CNow you already know P,C,S,t and I'm going to assume that you know the risk-free rate r.For each expiry date you can play with the different put-call pairs, trying values of d until all the put-call pairs for the same expiry give pretty much the same forward price, F. The value of d that gives the same F for all put-call pairs is the value of d to use when valuing options of that expiry date.

FDAXHunter and Johnny, Thanks a lot for your kind help , and the time taken.I have been trying to implement the following:"For each expiry date you can play with the different put-call pairs, trying values of d until all the put-call pairs for the same expiry give pretty much the same forward price, F. "I implemented it using Simplex optimization as:1.Objective function to minimize the variance of the forward rates ,using the mentioned equation.2.Parameter vector with a single parameter "d" 3.Constraint function to set "d" between -0.99 to .99 Unfortunately,I have a new problem now. The "d" value set to minimize the objective function always gets to the upper limit fo my boundary constraint. It tends to have the highest possible value, in order to bring the forward rates as close as possible.Perhaps I am doing wrong somewhere. Can you please suggest some tip?Thanks ,asd

I tried to take one more try, with modifying the objective function of the simplex method. I now set the objective function of the simplex method to minimize the value F - (S*exp(r*t))F : forward price calculated using "d" trial valueS : underlying r : zero yield obtained by linear interpolation of term structuret : time to maturity(years)The value now converges ,and I get the following value of "d" for different maturities:Date :10/17/2003 d : -0.059375Date :11/21/2003 d : -0.04375Date :12/19/2003 d : -0.0292812Date :01/16/2004 d : 0.0495Date :03/19/2004 d : -0.0285859Date :01/21/2005 d : -0.0220312Date :01/20/2006 d : -0.0270762But don't know if this is OK. Can "d" be so high?Following is the dividend info:Dividends & Splits Annual Dividend: 0.75 Dividend Yield: 2.58% Dividend Date: 10-Sep-03 Ex-Dividend Date: 18-Aug-03 Last Split Factor (new per old)²: 2:1 Last Split Date: 16-Sep-97 Thanks,asd

QuoteOriginally posted by: JohnnyI'm also delighted to see that you're looking properly at the forward rates. Let me suggest an alternative to FDAX's method. I'm pretty sure that this way is equivalent to the FDAX approach.1. Start with put-call parity:Share + Put = Bond + CallS + P = K.exp(-r.t) + C2. Write down an expression for the price of a forward:F = S.exp((r-d).t)Where d represents the total of dividend yield, dividend tax and stock borrow costs.3. Put these two expressions together:F.exp((d-r).t) + P = K.exp(-r.t) + CNow you already know P,C,S,t and I'm going to assume that you know the risk-free rate r.For each expiry date you can play with the different put-call pairs, trying values of d until all the put-call pairs for the same expiry give pretty much the same forward price, F. The value of d that gives the same F for all put-call pairs is the value of d to use when valuing options of that expiry date.I tried matching the forwards F for MSFT Jan 05 option quotes obtained from CBOE website, using the above formula F.exp((d-r).t) + P = K.exp(-r.t) + Cto match the implied forward prices for options of different strikes.Initially I set r=0.01Tried playing around with d, but the F's seem be in a curve do not appear to be close enough for all possible values of d being selected.Can someone please help? I have attached spreadsheet

if I understand correctly, you are having problems with your putcall parity where the underlying is a single stock.My first suggestion is to forget about using a dividend yield. In single stocks, it is normally better to use a discrete dividend model.The forward becomes:F = exp((r-b)T) (S -PVDIV)where r is the rate to maturty, b is the borrow cost to maturity (normally you can set that to zero), PVDIV is the present value of all the divs paid to maturity.Putcall parity remains the same: C-P = exp(-r T) (F-K)To check your machinery, I would them advise to plug in sensible estimate for PVDIV, r from a reasonable yieldcurve, b=0 (for very liquid stocks)and compute implied bid/ask vols for calls and puts. Plot them vs different strikes and you should see reasonably smooth curves (do not choose too short maturities of course), with call bids in line with put bids, etcOnce you are confident that all your tools are properly set up, then you can move on to more fancy stuff.

Granchio, Thanks a lot for your help. However, I am stuck at the initial stage itself, when trying to find the implied dividend yield of the MSFT stock, using the option quotes available for different strikes at a given maturity.No matter what values of "d" I try to use for implying the forward price, it seems that the graph of F versus strike is always sloping downwards => forward price decreases for increase in strike price with a curvature near ATM. Only the level of the curve is shifted upwards/downwards.Has it something to do with volatility Smile, or is it bad data, or I am doing wrong?? (My aim is to plot a local volatility surface for MSFT stock, but I don't know the dividend yield to pass into the implied volatility formula. )Thanks

asd,Why dont you describe how you proceed instead of providing numbers? For me it is quite unclear how you achieve 'prices'. I do not know much aboutthe US but i have seen quote machines (on european indices) producing fixedspread (in points) and sometimes more complicated figures around mid vola.So you can not just take the average. And for extreme cases: just kick it.The usual way to get impl div ... well, i would look for a consenus estimatesand you may find it directly and if you want it sophisticated through theoption market you can not simply use quotes or last prices.Even for the simplier case of _european_ style you need a desk & good rates:doing something similar (but converse) for indices (think of the Swiss SMIwhich has 'two dividend' components due to tax laws as ugly case). AroundATM you have: spot (note that fwd gives not uniquely the spot, otherwisearbitrage desk would not exist), rates and div. If you think (=the desk) thatall is ok, you can solve (try a triple of pairs around ATM), but it may be agood idea to check it especially against deep in the money (and if you do itgood enough your desk will find the amount caused by tax arbitrage againstDAX w.r.t. the EC and GB).For your american style problem at least you will use a _good_ options pricerbeyond BS. To get a vol surface the way is different: find divs first. First!Not through 'unknowns', that is unstable. Then get the prices (not from Joohoo,but from a desk). And then ... Hmm: how much is MS willing to pay (in div yield) and what is a move throughnews like a) EC wants money (monopoly= b) a change in licence policy c) sometechnological change d) ... ? Just my ideas on that.

Avt, Thanks a lot for your response."Why dont you describe how you proceed instead of providing numbers? "Sorry for not being clear! I use the method as described by Johnny's earlier post on Oct 2001 in this thread . Following are the steps I use:1. Start with put-call parity:Share + Put = Bond + CallS + P = K.exp(-r.t) + C2. Write down an expression for the price of a forward:F = S.exp((r-d).t)Where d represents the total of dividend yield, dividend tax and stock borrow costs.3. Put these two expressions together:F.exp((d-r).t) + P = K.exp(-r.t) + CI assume r=0.01 ,set t= year fraction of option maturityd = trial valueC = CallBidP = PutBid and calculate values of F for different strikes at a given maturity using:F = (K.exp(-r.t) + C - P*exp((r-d).t)Thanks again for your help and valuable tips.Regards,Asd

asd,May be i was too unclear, sorry.For american styles you can not use P/C parity except you know exercise time,that's what i meant with a good pricer. If you want to use P/C you need 'fair'prices and can not work with ask/bid (and without time stamp against spot).AFAIK for M$ div is yearly and around 0.7%, so if you take _supposed_ rates of1.0% you will have a hard job to extract a precise value for the divs beyondconsensus estimates (even with exact rates) - but may be i understood youwrong here?Now a look at the data (you have them for Jan 05): the puts for 55 ... 80 dohave a fixed spread x.16 vs x.80 - what do you want to use as that are notprices? Moreover you see no bid for the calls beyond 40, ignore it? Or haveyou thought about the simple rule 'call below banking then exercise put'?On the downside P for 12.5 and 15.0 also has a spread of 0.18 ... More or less i would try to look around ATM i.e. 27.5, 30.0 and 32.5 firstand then see whether the rest fits without pain. But as stated: this datasource is not very useful for several reasons.Axel Edited: and as granchio said it is better to obey discrete div payments.

Hey people, one dumb question: Would the results be very different if dividends were implied directly from futures prices, instead of puts and calls ? Would this approach imply different assumptions / models ? Thanks for your help,

Anyone on this question ?