1.Principal Components Analysis (PCA) is a multivariate statistical technique that is used further as a dimension reduction technique. You could use PCA to identify the drivers of the response, which are called principal components. The principal components are not actual variables but rather hypothetical constructs (or factors similar to factors in factor analysis) that are ordered in terms of most explanatory to least explanatory. Typically, the first 2-3 components explain a significant amount of the information in the data, so the statistician makes a decision with respect to to how many components to utilize. PCA is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix. PCA is the simplest of the true eigenvector-based multivariate analyses.
2. Effective Duration
Duration is the approximate percentage change in price for a 100 basis point change in rates. To compute duration, you can apply the following equation that was presented earlier in the guide.
Price if yield decline - price if yield rise / 2(initial price)(change in yield in decimal)
Effective duration takes into account the way in which changes in yield will affect the expected cash flows. It takes into account both the discounting that occurs at different interest rates as well as changes in cash flows. This is a more appropriate measure for any bond with an option embedded in it.
3."Full revaluation method calls for revaluation of the derivative at Var of the underlying" while Jorion says"Full valuation methods measure risk by full re-pricing the portfolio over a range of scenarios". This repricing could be done using risk factors generated by historical stimulation or Monte Carlo methods or Boot Strapping.
4. The delta is a ratio comparing the change in the price of an asset, usually a marketable security, to the corresponding change in the price of its derivative. Delta values can be positive or negative depending on the type of option.
For example, the delta for a call option always ranges from 0 to 1, because as the underlying asset increases in price, call options increase in price. Put option deltas always range from -1 to 0 because as the underlying security increases, the value of put options decrease. For example, if a put option has a delta of -0.33, if the price of the underlying asset increases by $1, the price of the put option will decrease by $0.33. Technically, the value of the option's delta is the first derivative of the value of the option with respect to the underlying security's price.
5.To effectively neutralize the gamma, we first need to find the ratio at which we will buy and write. Instead of going through a system of equation models to find the ratio, we can quickly figure out the gamma neutral ratio by doing the following:
Find the gamma of each option.
To find the number you will buy, take the gamma of the option you are selling, round it to three decimal places and multiply it by 100.
To find the number you will sell, take the gamma of the option you are buying, round it to three decimal places and multiply it by 100.
For example, if we have our $30 call with a gamma of 0.126 and our $35 call with a gamma of 0.095, we would buy 95 $30 calls and sell 126 $35 calls. Remember this is per share, and each option represents 100 shares.
Buying 95 calls with a gamma of 0.126 is a gamma of 1,197 (9,500*0.126).
Selling 126 calls with a gamma of -0.095 (negative because we're selling them) is a gamma of -1,197 [12,600*(-0.095)].
6. Position delta can be understood by reference to the idea of a hedge ratio. Essentially, delta is a hedge ratio because it tells us how many options contracts are needed to hedge a long or short position in the underlying. By changing the ratio of calls to number of positions in the underlying, we can turn this position delta either positive or negative.
For example, if an at-the-money call option has a delta value of approximately 0.5 - which means that there is a 50% chance the option will end in the money and a 50% chance it will end out of the money - then this delta tells us that it would take two at-the-money call options to hedge one short contract of the underlying. In other words, you need two long call options to hedge one short futures contract. (Two long call options x delta of 0.5 = position delta of 1.0, which equals one short futures position). This means that a one-point rise in the S&P 500 futures (a loss of $250), which you are short, will be offset by a one-point (2 x $125 = $250) gain in the value of the two long call options. In this example we would say that we are position-delta neutral.