# Report of Dynamic Hedging

Topics: Option, Implied volatility, Volatility smile Pages: 7 (1663 words) Published: January 14, 2013
[键入公司名称]|
Report|
Dynamic Hedging and Implied Volatility|
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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

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 out-of-the-money. 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 B-S price. And also how accurate the B-S price is. According to the statistic analysis below, I think portfolio insurance is feasibility.

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