In the world of mathematical finance, an important skill for any quantitative analyst is to price derivatives. These usually come in the form of options as well as other more exotic financial instruments. For this project we will focus on something called European Call options. We will see how you can estimate the price of an underlying asset (usually a stock) at some time in future T and use this to find how much an option should cost today. First, lets take a look at what a European call option actually is. The idea behind the European call option is that you will enter into a contract with someone that grants you the right, but not the obligation, to purchase some number of shares of a stock at a pre-determined price, called the strike price. In this paper we will say that the payoff for a European call option can be given by: max {S(t) – K, 0}. The reason we do this is because, it would not make sense to exercise the option if the price of the
In the world of mathematical finance, an important skill for any quantitative analyst is to price derivatives. These usually come in the form of options as well as other more exotic financial instruments. For this project we will focus on something called European Call options. We will see how you can estimate the price of an underlying asset (usually a stock) at some time in future T and use this to find how much an option should cost today. First, lets take a look at what a European call option actually is. The idea behind the European call option is that you will enter into a contract with someone that grants you the right, but not the obligation, to purchase some number of shares of a stock at a pre-determined price, called the strike price. In this paper we will say that the payoff for a European call option can be given by: max {S(t) – K, 0}. The reason we do this is because, it would not make sense to exercise the option if the price of the
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
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Transcribed Image Text:In the world of mathematical finance, an important skill for any quantitative analyst
is to price derivatives. These usually come in the form of options as well as other more
exotic financial instruments. For this project we will focus on something called European
Call options. We will see how you can estimate the price of an underlying asset (usually a
stock) at some time in future T and use this to find how much an option should cost today.
First, lets take a look at what a European call option actually is.
The idea behind the European call option is that you will enter into a contract with
someone that grants you the right, but not the obligation, to purchase some number of
shares of a stock at a pre-determined price, called the strike price. In this paper we will say
that the payoff for a European call option can be given by: max {S(t) – K, 0}. The reason we
do this is because, it would not make sense to exercise the option if the price of the
underlying asset is below the strike price, K. Suppose that you could purchase shares on
the open market at $10 per share, but your strike price was set at $12, you would not pay
more money for the stock, if you didn't have to do that.
In the space below, sketch the payoff function that is described by max{S(T) – K, 0}.
Explain why your sketch makes sense:
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