## In this task, you should calculate the price of a so-called warrant, which is a financial instrument very similar to an option

### computer science

##### Description

In this task, you should calculate the price of a so-called warrant, which is a financial instrument very similar to an option, the difference being that a publisher (usually a bank) stands as a guarantor to sell and buy the warrant at a given time. In the case of the option, there must be (like for example a share) a buyer who meets a seller and there is therefore no guarantee to be able to buy or sell one at a given time (low trading volume). For the warrant, however, the publisher takes a financial risk unlike stock trading where (the online bank) is only a broker and takes a brokerage. To price this risk, Black-Scholes formula is implemented in matlab in "finance toolbox":

[Call, Put] = blsprice (Price, Strike, Rate, Time, Volatility)

"Call" is the price of a purchase warrant. "Put" is the price of a sales warrant. "Price" is the current price of the underlying stock. "Strike" is the exercise price for the underlying stock. "Rate" is "risk-free interest rate", assume 2%.

"Time" is the time until the warrant expires (unit number of years eg 0.5 for 6 months). "Volatility" is the volatility of the underlying stock which is defined as follows: - from closing prices x for n days form the differences (x2-x1) / x1, (x3-x2) / x2 ,. . . (Xn-xn-1) / x n-1 - calculate the standard deviation of the natural logarithm of these values - multiply this by the root of 252 (= ~ number of trading days in one year) Your task is to use the given data file with price data for a share for a period of time and calculate what the purchase and sale warrants would cost for that share. You should calculate these for a strike price that varies by -50% to + 50% (in increments of 25%) from the current share price and for a period of time from 0.1 years to 2 years. There will be a graph for each strike price and warrant type where the time is on the x-axis and the warrant price on the y-axis, draw 10 graphs. You can draw several in the same graphics window. Is the result reasonable? Feel free to compare with warrant prices you find online