Report
Dynamic Hedging and Implied Volatility

sony


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
Fitting Graph of X=90
The smallest difference is 0.14 (10/18). 8 out of 15 observations’ difference are smaller than one. The track is not as good as the previous one. Furthermore, the fitting graph shows that the synthetic price tracks the actual call price not well. * 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=0.85*P.F Value+1.03
t=5.724 20.18 R Square=0.99
This regression gets a pretty precise result as each t is larger than 2 and R square is 0.99. The result shows that the coefficient is 0.85 and the constant is 1.03, and this one tracks worse than X=87.5. * Correlation coefficient
 Call Price P.F Value
Call Price 1 
P.F Value 0.9596304 1
The two prices are highly correlated. However, X=90 tracked worse than X=87.5 as the coefficient is smaller.
b. Any comments (if relevant) concerning the relative behavior of two options (did one synthetic option portfolio perform better than the other?) The X=87.5 synthetic option did better than the X=90. I think one reason is the X=90 call out of money in the last a few days. According to the fitting graph of X=90, the difference become lager since the call outofthemoney. Besides, the only difference between these two options is the exercise price. c. A short commentary of the feasibility of portfolio insurance based on your experience with the option you chose (conclusions may differ across participants in the project). Use some type of statistical analysis in drawing your conclusions.
In my view, the main point to illustrate feasibility is how close the portfolio value is close to BS price. And also how accurate the BS price is. According to the statistic analysis below, I think portfolio insurance is feasibility.
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