Report of Dynamic Hedging
[键入公司名称] | Report | Dynamic Hedging and Implied Volatility | | sony | |
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Part I
Dynamic Hedging 1. Basic Information Company | 3M Co. (MMM) | Two different options to mimic | 1) X=87.5 call option, expiring at Nov 16, 2012. 2) X=90 call option, expiring at Nov 16, 2012. | 2. Calculate the annualized standard deviation: σ=0.1357502 Completed calculation table (See Appendix) 3. Replicating Portfolios
X=87.5 call option
Completed calculation table (See Appendix)
X=90 call option
Completed calculation table (See Appendix) a. A discussion of how well the synthetic option price tracked the actual option price for each of the options; include some sort of empirical analysis in support of your discussion
1) X=87.5 call option
* Description analysis
Fitting Graph of X=87.5
The table above describes the prices of actual call price, portfolio value and the difference (P.F value minus call price) respectively. The smallest difference is 0.07 (10/22). 12 out of 15 observations’ difference are smaller than one. The track is not perfect but just ok. Furthermore, the fitting graph shows that these two prices are similar. * Empirical analysis
Assume the regression model: call price=β*P.F Value+c β: coefficient describes the relationship between call price and P.F Value
Then doing the regression analysis through Excel and getting the result as followings: call price=0.86*P.F Value+0.96 t=20.18 5.72
R Square=0.97
This regression gets a pretty precise result as each t is larger than 2 and R square is 0.97. The result shows that the coefficient is 0.86. The two prices are not exactly the same and they are just pretty much close. * Correlation coefficient | Call Price | P.F Value | Call Price | 1 | | P.F Value | 0.984409542 | 1 |
The two prices are highly correlated.
2) X=90 call option * Description analysis
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Part I
Dynamic Hedging 1. Basic Information Company | 3M Co. (MMM) | Two different options to mimic | 1) X=87.5 call option, expiring at Nov 16, 2012. 2) X=90 call option, expiring at Nov 16, 2012. | 2. Calculate the annualized standard deviation: σ=0.1357502 Completed calculation table (See Appendix) 3. Replicating Portfolios
X=87.5 call option
Completed calculation table (See Appendix)
X=90 call option
Completed calculation table (See Appendix) a. A discussion of how well the synthetic option price tracked the actual option price for each of the options; include some sort of empirical analysis in support of your discussion
1) X=87.5 call option
* Description analysis
Fitting Graph of X=87.5
The table above describes the prices of actual call price, portfolio value and the difference (P.F value minus call price) respectively. The smallest difference is 0.07 (10/22). 12 out of 15 observations’ difference are smaller than one. The track is not perfect but just ok. Furthermore, the fitting graph shows that these two prices are similar. * Empirical analysis
Assume the regression model: call price=β*P.F Value+c β: coefficient describes the relationship between call price and P.F Value
Then doing the regression analysis through Excel and getting the result as followings: call price=0.86*P.F Value+0.96 t=20.18 5.72
R Square=0.97
This regression gets a pretty precise result as each t is larger than 2 and R square is 0.97. The result shows that the coefficient is 0.86. The two prices are not exactly the same and they are just pretty much close. * Correlation coefficient | Call Price | P.F Value | Call Price | 1 | | P.F Value | 0.984409542 | 1 |
The two prices are highly correlated.
2) X=90 call option * Description analysis