FINS 2624 Study Notes Compressed

A similar study was performed by kothari shanken

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Unformatted text preview: ns to estimate σ. For example, if the option expiration date is in 90 days, we will collect the daily stock prices of the past 90 days and then compute the SD of CCR. To convert the SD of CCR to an annualized figure, we do: √( )( ). T HE MEANING OF XE -R T Xe-rt is the present value of the exercise price of an option, where e-rt is the present value factor that uses a continuously compounded discount rate. An investor who would like to defer the purchase of a stock may buy a call option today. By further setting aside a deposit which will guarantee an amount of $X at maturity, the investor is guaranteed to have sufficient funds in the future to purchase the stock. If S*>X, the investor can use $X in the deposit account to purchase the stock. If S*<X, the investor can purchase the stock at S* and have money to spare. Similar, in terms of a put option, an investor who would like to defer the sale of a stock may buy a put option today. By borrowing an amount which $X must be paid off at maturity, the investor is guaranteed to have sufficient funds to pay back. If S*>X, then the investor can sell the stock into the market at $S* and have money to spare. If S*<X, then the investor may exercise the right to sell the stock at $X and have money to repay the debt of $X. T HE UNIT NORMAL DISTRIBUTION A normal distribution is a continuous bell shaped probability distribution that is symmetrical at its mean. The bell shaped curve is called the normal density function. For a unit normal distribution, the mean is 0 and the SD is 1. N(x) is the area under the curve from minus infinity to a given standardized value of x. Since the probability of observing all possible values is 1, the probability of observing an outcome with a value greater than x is 1 – N(x). ̅ To standardize and find x, use the formula - T HE MEANING OF D 2 Black and Scholes showed that the natural logarithm of stock price is normally distributed with: Mean = ln S + (r – 0.5σ2)t Standard Deviation = σ√ Hence, to find the probability of seeing a call option finish in the mone...
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