# 微积分网课代修|导数代写Derivatives theory代考|AFIN546 OPTIONS

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分网课代修导数代写Derivatives theory代考|OPTIONS

Options are a little more difficult to understand than forwards and futures and here we present a quick introductory overview. While futures markets in commodities have existed since the middle of the $1800 \mathrm{~s}$, options contracts have been traded for a shorter period of time. There are two types of option, calls and puts:
The holder of a call (put) option has the right (but not an obligation) to buy (sell) the ‘underlying asset’ at some time in the future (‘maturity date’) at a known fixed price (the ‘strike price’, $K$ ) but she does not have to exercise this right.

For the moment we consider stock option contracts, so the underlying asset in the option contract is the stock of a particular company-XYZ which is traded on the NYSE. The option contract itself, we assume is traded in Chicago.

Above we noted that the holder of a long futures contract on a stock-XYZ commits herself to buy the stock at a certain price at a certain time in the future and if she does nothing before the maturity date, she will have to take delivery of stock-XYZ, at the pre-agreed futures price. In contrast, the holder of a (European) ‘call option’ on stock-XYZ can decide whether to pay the known strike price and take delivery of stock-XYZ on the maturity date of the option contract – this is called ‘exercising the option contract by taking delivery’. If it is advantageous not to exercise the option (in Chicago) then the holder of the call option will simply do nothing. For the privilege of being able to decide whether or not to take delivery of stock-XYZ (at maturity of the option contract) the buyer of the call option must pay an upfront, non-refundable fee – the option price (or premium).

## 微积分网课代修导数代写Derivatives theory代考|Call Options

If today you buy a European call option and pay the call premium/price, then this gives you the right (but not an obligation):

to purchase the underlying asset

at a designated delivery point

on a specified future date (known as the expiration or maturity date)

for a fixed known price (the exercise or strike price)

and in an amount (contract size) which is fixed in advance.For the moment, think of a call option as a ‘piece of paper’ that contains the contract details (e.g. strike price, maturity date, amount, delivery point, type of underlying asset). You can purchase this contract today in the options market in Chicago if you pay the quoted call premium. There are always two sides to every trade – a buyer and a seller – but we will concentrate on your trade, as a buyer of the option. Note that all transactions in the option contract

are undertaken in Chicago but the underlying asset, for example a stock, is traded on another exchange (e.g. NYSE).

Suppose the current price of stock-XYZ on the NYSE on $15 \mathrm{July}$ is $S_{0}=\$ 80$. On 15 July you can pay the call premium$C=\$3$ and buy (in Chicago) an October-European call option on the stock-XYZ. The strike price in the contract is $K=\$ 80,{ }^{4}$and the expiry date$T$is in just over 3 months’ time on 25 October. Because the maturity of the call is in October, and the strike is$K=\$80$, it is known as the ‘October- 80 call’ (Table 1.4). Assume each call option is for delivery of one stock of XYZ.