【原】(英文)笔记:有关期权的基本知识

Abstract

In this part, we will mainly learn the definition and properties of options.Then,we will also talk about some functions of options.

Types and definition of options(期权的定义和类型)

Firstly,we should learn the definition of options.

「Definition1」(options):an agreement that the holder can buy from(or sell to ) the seller (the buyer)of the option at a specified future time a certain amount of an underlying asset at a specified price.But the holder is under no obligation to exercise the contract.

「Remark」:In fact, the holder has to pay premium for this right.Moreover, options has a much higher level of leverage.

Then, we should master  two option:call option and put option.

「Definition2」(call option and put option):

• A call option(看涨期权)- a contract to buy at a specified future time a certain amount of an underlying asset at a specific price;
• A put option(看跌期权)- a contract to sell at a specified future time a certain amount of an underlying asset at a specific price;

「Remark」:From these definitions, we can easily find that the difference of both options is "buy" or "sell". If you want to buy , it means that the option is rising.

「Definition3」(exercise price,expiration,exercise): We define exercise price(实施价格) as the specified price,and we define expiration date(到期日) as the specified time

But what's the meaning of exercise(实施)? Exercise is the action to perform the buying or selling of the asset according to the option contract.

In fact, if the options are divided according to the terms of the implementation of the contract,then we can get: European options and American options.

「Definition4」(European options and American options):

• European options(欧式期权)- can be  exercised only on the expiration date.
• American options(美式期权)- can be exercised on or prior to the expiration date.

「Remark」:Besides above both options, there are other options such as Asia option.

「Total Gain of an Option」:[Total gain]=[gain of the option at expiration]-[premium].

• Call option:;
• put option:.

where stands for premium(期权金),stands for strike price,stands for the price of the underlying asset at expiry date .

Properties of options

It is easy to find that the price of risky asset  is a random variable, the price of any option derived from risky asset is also random,and the price also depends on time .If the price of the underlying asset is ,the price of option is ,then there exists a function  such that

As is known to all,

When ，if the share price is ,then we may ask a question:how to find out ?

Functions and examples about options

1. 「Hedger(套期保值者)」-to invest on both sides to avoid loss;

2. 「Speculator(投机者)」-to take action characterized by willing to risk with one's money by frequently buying and selling derivatives(futures,potions)for the prospect of gaining from the frequent price changes;

3. 「Arbitrage(套利者)」-based on observations of the same kind of risky asset, taking advantage of the price differences between markets,the arbitrageur trades simultaneously at different markets to gain risk-free instant profits.

 Course summary(课程小结): 

I have learnt the definition and types of options,and simultaneously grasped some properties and functions of options.In order to price for options, we establish a binary function . In particular, is a stochastic process with regard to .In this lesson, The affairs of China Aviation Oil are so profound that I'm impressed with this lesson.Similarly, when Teacher Liang cited the story of software companies which always write arbitrage software, I think arbitrage are smart and realize a word,"Venture investment is a profit-pursing operations of capitals". In fact, this lesson will help us understand financial risks and options pricing better . Although the theory of options pricing is the core of Financial Engineering, it seems that mathematical tool is not frequently used. However, In my perspective, it is essential and reasonable for us to set up a partial differential equation to determine this function , this is my tremendous benefits in this lesson.