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UA MATH 115A - Quiz Study Guide

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Study Guide—Project 2 Quiz: OptionsBackground Information- What is an option?- What are the different types of options?o Put Options vs. Call optionso American Options vs. European Options- When do these options expire?- When can an option be exercised?- What does the strike price tell you?- What is the value of an option on the expiration date?oSCV  where C is the closing price of the stock on expiration date and S is thestrike price of the optionProject Related- Compound InterestontnrPF 1ortPeF ontnrFP 1ortFeP- Risk-free rate (r): rate of return guaranteed by the US Treasuryo Weekly risk-free rate: 52rrrf- The ratio of the future value to present value PFR o For continuous compounding: rrePPeR  Project rfR was called the risk-free weekly ratio of our stock. This value was based on the US Treasury weekly risk-free rate: rfrrfeR o Use: allows us to convert the interest rate for a given period to a ratio of future to present value for the same period.o In our project, we determined a series of observed ratios by finding the adjusted closing price of our stock and dividing it by the previous week’s adjusted closing price. This number told us by what factor the stock grew (or lost) value between those two consecutive weeks- Normalizing & normRo According to assumption 1 the closing price a stock on the expiration date cannot be predicted.o Assumption 2 says that the volatility of our stock can be used to predict future volatility. In our project we are using the ratios between consecutive weeks as a measure of our stock’s volatility. You should be able to tell if from a histogram of the normalized ratios whether one stock is more volatile than another.o Unfortunately, these ratios still rely on the past closing prices of our stock.o Assumption 3 says that all stock which can be predicted probabilistically are to have the same rate of returno That rate of return according to assumption 4 is the risk-free rate guaranteed by the US treasuryo Because of we need to normalize our observed ratios R so that  rfRRE . We did this by doing the following calculation: rfmnormRRRR  where mR is the mean of our observed ratioso Doing this preserved the overall volatility of the stock but removed the underlyinggrowth rate that was associated with the historical data of each stock. Normalizing then was the way in which we brought all stocks to a common meansof comparison.Excel Functions• Sort (under Data)• Histogram (under Tools – Data Analysis)• MIN/MAX (Statistical)• COUNT (Statistical)• BINOMDIST (Statistical)• RANDBETWEEN (Math & Trig)• VLOOKUP (Lookup & Reference)• COUNTIF (Statistical)• RAND (Math & Trig)• IF (Logical)Random Sampling & Simulations- Using histogram to approximate a probability density functiono The height of each bar is the relative frequency (rf) divided by the bin width (bw) Height = wfbro The total area of all the rectangles on the histogram is equal to 1 The area of any one rectangle is the relative frequency:-fwfwrectrbrbA - Sample mean of a random variable is an approximation of the expected valueo x All1ixnXEo The larger your random sample is the better your approximation- Computer simulation is a time-efficient way to predict the behavior of certain quantities in an experiment without actually doing the experiment.o You should be able to the VLOOKUP, RANDBETWEEN functions as we did in our


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UA MATH 115A - Quiz Study Guide

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