a) Define an Asset base class that provides the following method:
class Asset
{
public:
virtual double getValue()=0;
};
This will be the base class for both stock and options classes.
b) Create a Stock class that inherits from Asset. This class should return the stock price as the value for getValue(). You should define a method to set the stock value as well. In the exercises below, use this class instead of passing stock prices as parameters. It may also be natural to have other stock attributes in this class.
c) Define four Asset child classes:
a. AmericanCall - a call option with early exercise
b. EuropeanCall - a call option with exercise only allowed at option expiration
c. AmericanPut - a put option with early exercise
d. EuropeanPut - a put option with exercise only allowed at option expiration.
It is up to you to decide upon a suitable class inheritance structure. You will also probably find it useful to create one or more parent classes to encapsulate functionality.
Each option class should (eventually) implement its own getValue() function based on the type of option and whether early exercise is allowed. You will need the binomial tree from Part II to implement getValue() for American style options. You may find it useful to initially make these functions 'dummies' (i.e. ones that return a constant) until the binomial tree is implemented.
d) Add a BlackScholesValue function to EuropeanCall and EuropeanPut that implements the closed form solution of each. Note: since we will not be varying the risk-free rate or stock volatility, this method might also be useful for getValue() for these options.
e) Create a method ValueSpots(double lowerSpotPrice, double upperSpotPrice, int numberOfSpots, char Name[]) that, for the European Call and European Put, writes numberOfSpots option values to a file whose name is specified by Name. The function should start with a stock price of lowerSpotPrice and ending with upperSpotPrice. The spot prices should be equally spaced.
Each line of the file should have the following format:
, Strike, Spot, Sigma, T, r, Price
where is a two character description of the option type. Use EC for a European Call, EP for a European Put, AC for an American Call and AP for an American Put. You won't calculate the values of American Calls and American Puts until part II, but we use the terminology here.
For example, assume for a European Put with stock spot price of $81 you calculate the put value to be $21.02. Then the line in your file would be:
EP, 100, 81, 0.4, 1.0, 0.05, 21.02
Execute the function for both European Puts and Calls with Strike $100, Sigma = 40%, risk-free rate = 5% and T = 1 Year, varying the spots from $75 to $125, thereby generating 51 values.