Business and Option Valuation
[对应中文教材 2008 年财务成本管理第十章:企业价值评估、第十一章:期权估价]
main features of options（期权的主要特征）
An option gives its holder the right（but not the obligation）to buy or sell a specific quantity of a
specific asset at a fixed price on or before a specified future option is purchased by the option
holder and is sold by the option ‘writer’.
期权是指一种合约，该合约赋予持有人在某一特定日期或该日之前的任何时间以固定价格购进
或售出一种资产的权利。
Exchange-traded and OTC options
Options might be bought and sold on an options exchange such as LIFFE[LONDON
INTERNATIONAL FINANCIAL FUTURES EXCHANGE:伦敦国际金融期货交易所]，or arranged
‘over-the-counter’[场外交易] with a -traded options include options on equity shares and
options on futures currency options are also exchange traded，for example on the
Philadelphia Stock Exchange[费城交易所].Interest rate options and most currency options are
over-the-counter（OTC）options.
A feature of exchange—traded options is that，like futures contracts，they are standardized
instruments.[标准化的工具]
OTC options，in contrast，are tailored to the specific requirements of the option buyer.
Calls and puts
Options are either call options or put options（or a combination of a call and a put）.
A call option gives its holder the right，but not the obligation，to buy the underlying item at the
specified price.
Call option: 买入选择权;买入期权;看涨期权;
A put option gives its holder the right，but not the obligation，to sell the underlying item at the
specified price.
Put option: 卖出选择权;卖出期权;看跌期权;
An option is a contractual the holder（持有者） of an option exercise（行使权利）
the option，the seller or writer（与 seller） of the option must fulfill his side of the contract，and sell（call
option）or buy（put option）the underlying item（期权的标的资产） at the agreed price.
Expiry date：European-style and American-style options （欧式和美式）
Strike price or exercise price[执行价格]
In-the-money（赚钱）[实值状态,溢价状态] and out-of-the-money options（赔钱）[虚值状态,
折价状态]
At the money（照所付的代价）[平价期权,平价状态]
An option will only ever be exercised if it is in-the-money.
Option premium[期权价格/成本]
An option is purchased by the buyer from the option seller or purchase price is called the
option premium.
A position in options can be opened by buying options to hold a long position or selling options to
create a short long or short position can be held in either calls or puts.
The value of an option[期权价值]（its premium or current market value）is said to consist of two
elements：
Intrinsic value[内在价值]
Time value[时间溢价]
Intrinsic value is the difference between the strike price for the option and the current market price of
the underlying item.[内在价值的大小,取决于期权标的资产的现行市价与期权执行价格的高低.]Only
an in-the-money option has an intrinsic value， value cannot be negative，so an
out-of-the-money option has intrinsic value of 0.
Time value is the value placed on the option. [期权的时间溢价是指期权价值超过内在价值的部分]
Time value depends on factors such as：
The period of time remaining to the option's expiry date.[到期期限]
The volatility of the market price of the underlying item.[股票价格的波动率]
For an out-of-the-money option，the extent to which the underlying market price must move before
the option becomes in-the-money.
pricing[期权定价]
Value of a call option[看涨期权]
The major factors in determining the price of a call option are as follows：
The price of the underlying instrument and the exercise ，it is the difference
between the strike price and the underlying market price that matters.[期权标的物的价格和执行价格]
The higher the price of the underlying instrument，the more valuable the call option，and the lower
the exercise price the more valuable the call option
The time to go to longer the remaining period to expiry，the greater the probability that
the underlying instrument will rise in value.[距离到期日时间]
The volatility of the underlying greater the volatility of the price of the underlying
instrument the greater the probability of the option yielding is another aspect of the time value
of an option.[期权标的价格的变动]
Interest rates[利率]
Whether a European option or an American option.[欧式还是美式]
The Black-Scholes option pricing model[布莱克——斯科尔斯期权定价模型]
Lct Ps=the price of the underlying instrument,c, current share price if pricing an equity call
option
N（di）=the probability that a normal distribution is less than di standard deviations above the mean
X=the exercise price
r=the risk free interest rate.（NB Quote this as an annual rate as a decimal number）
T=the time to expiry（again quoted in years）,so that for a six-month option T and for a
three-month option
σ=the standard deviation of the underlying instrument’s returns
Then the basic form of the Black-Scholes model gives the value of a European call option as；
Example
The current share price of Moss plc is￡ the value of a European call option on the
shares of the company，with an exercise price of￡，and has 6 months to run before it risk
free rate of interest is 6%and the variance of the rate of return on the share has been l 5%.
[答疑编号 811080201]
Solution
First we calcutate d1 and d2,
We are given the variance of returns on the share, so take the square root to get the standard deviation.
Using a calculator, we can calculate the value of the natural logarithm of is .
Round this to （two decimal places）
Having calculated values for d1 and d2,we can now go on to calculate the option price,
Optioion price=（）×××N（）
（using a calculator）.
To establish the value of N（d1）when ,refer to the normal distribution tables.
This shows a value of Since d1 is greater than 0,and to get ,In the calculation
below, this is rounded down to .
Similarly, to calculate a value for N（d2）,when ,we look up the value of in the normal
distribution gives us . This is rounded down to in the following price calculation.
You might like to see the normal distribution calculation shown graphically.
So N（）=+=
Asset valuation bases
The net assets valuation method can be used as one of many valuation methods, or to provide a lower
limit for the value of a company. By itself it is unlikely to produce the most realistic value.
Choice of valuation bases
Possibilities include:
Historic basis
Replacement basis
Realizable basis
based valuation bases
P/E ratios are used when a large block of shares, or a whole business, is being valued. This method
can be problematic when quoted companies’ P/E ratios are used to value unquoted companies.
The P/E ratio （earnings） method of valuation
This is a common method of valuing a controlling interest in a company, where the owner can decide
on dividend and retentions policy. The P/E ratio relates earnings per share to a share's value.
Since P/E ratio = Market value/EPS
then market value per share = EPS ×P/E ratio
Earnings per share （EPS）
= profit/loss attributable to ordinary shareholders / weighted average number of ordinary shares
The earnings yield[盈余报酬率,市盈率 price earning ratio 的倒数] valuation method
Another income based valuation model is the earnings yield method.
This method is effectively a variation on the P/E method （ the EY being the reciprocal of the P/E
ratio）, using an appropriate earnings yield effectively as a discount rate to value the earnings:
We can incorporate earnings growth into this method in the same way as the growth model.
This formula is given on your formula sheet as
flow based valuation models
The dividend valuation model-
The dividend valuation model is based on the theory that an equilibrium price for[均衡价格 ] any
share （or bond） on a stock market is:
The future expected stream of income from the security
Discounted at a suitable cost of capital
Equilibrium market price is thus a present value of a future expected income stream. The annual
income stream for a share is the expected dividend every year in perpetuity.
The basic dividend-based formula for the market value of shares is expressed in the dividend
valuation model as follows:
Where MV=EX dividend market value of the shares
D=constant annual dividend
Ke=shareholders’ required rate of return
The dividend growth model
Using the dividend growth model we have:
Where
D0 = Current year's dividend
g = Growth rate in earnings and dividends
D0（1 + g） = Expected dividend in one year's time （D1）
ke = Shareholders' required rate of return
P0 = Market value excluding any dividend currently payable
Discounted cash flow basis of valuation
This method of share valuation may be appropriate when one company intends to buy the assets of
another company and to make further investments in order to improve cash flows in the future.
