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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

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 3SE: The Oxford Dictionary defines the word nominal asa value that is “stated or expressed but...
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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:
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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