FE621 Computational Finance

1.编写一个函数（程序）以连接到源并下载数据

（b）雅虎财经
（c）彭博社

1个

2.使用在问题1中创建的功能，在两个选项上下载数据

•AMZN
•间谍
•VIX

DATA1（第一天）和DATA2（第二天）

3.编写一段描述您要为其下载数据的符号的段落。

ETF）。解释什么是VIX及其目的。了解如何
2

4.还需要记录以下各项：
•相关股票或ETF的确切价格

•可在此处获得的短期利率

（历史）利率。
•成熟时间。
Part 2. (50 points) Analysis of the data.
5. Using your choice of computer programming language implement the
Black-Scholes formulas as a function of current stock price S0, volatility
σ, time to expiration T − t (in years), strike price K and short-term
interest rate r (annual). Please note that no toolbox function is allowed
but you may use the normal cumulative distribution function (CDF)
calculation.
6. Implement the Bisection method to find the root of arbitrary functions.
Apply this method to calculate the implied volatility on the first day
you downloaded (DATA1). For this purpose use as the option value the
average of bid and ask price if they both exist (and if their corresponding volume is nonzero). Also use a tolerance level of 10−6
. Report the
implied volatility at the money (for the option with strike price closest
to the traded stock price). You need to do it for both the stock and the
3
ETF data you have (you do not need to do this for VIX). Then average
all the implied volatilities for the options between in-the-money and
out-of-the-money.
Note. There is no clearly defined boundary between options at-themoney and out-of-the-money or in-the-money options. If we define
moneyness as the ratio between S0 the stock price today and K the
strike price of the option some people use values of moneyness between
0.95 and 1.05 to define the options at the money. Yet, other authors
use between 0.9 and 1.1. Use these guidelines if you wish to determine
which options’ implied volatilities should be averaged.
7. Implement the Newton method/Secant method or Muller method to
find the root of arbitrary functions. You will need to discover the formula for the option’s derivative with respect to the volatility σ. Apply
these methods to the same options as in the previous problem. Compare the time it takes to get the root with the same level of accuracy.
8. Present a table reporting the implied volatility values obtained for every
maturity, option type and stock. Also compile the average volatilities
as described in the previous point. Comment on the observed difference
in values obtained for AMZN and SPY. Compare with the current value
of the VIX. Comment on what happens when the maturity increases.
Comment on what happen when the options become in the money
respectively out of the money.
9. For each option in your table calculate the price of the different type
(Call/Put) using the Put-Call parity (please see Section 4 from [?]).
Compare the resulting values with the BID/ASK values for the corresponding option if they exist.