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| Home > Options
/ Warrants Calculator |
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| If you wish to know more about stock options and
index options traded on HKEx, please go to the the Options
ABC section. There are also plenty of useful information about stock
options and index options posted on the website of HKEx at www.hkex.com.hk. |
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As discussed in the Options ABC session, the theoretical value
of a an option is affected by a number of factors such as the underlying stock
price/index level, strike price, volatility, interest rate, dividend and time
to expiry.
The availability of option pricing models allows us to determine the theoretical
value of an option. In this session, you will be able to compute the theoretical
value of an option by inputs of different variables and find out how the theoretical
value may vary with changes to the variables.
Please note that the calculator should not be used for pricing actual options/warrants
that you are about to buy or sell as the actual market environment may not be
the same as what the theoretical models assumed. |
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| The calculator is based on the commonly used Binomial Model
and Black-Scholes Model. The Binomial Model takes into account the dividend payments.
If the user does not input dividend values, zero dividend payments will be assumed
during the computation. The Black-Scholes Model is also available but dividend
payments are ignored in the computations. |
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| Inputs |
| INPUTS |
ACCEPTABLE
RANGES |
| Stock Price (S) |
0 < S < 20,000 |
| Strike Price (X) |
0 < X < 20,000 |
| Volatility (V) |
0% < V < 500% |
| Interest Rate (R) |
0% < R < 200% |
| Value Date (VD) |
Must be valid dates |
| Expiry Date (ED) |
ED >= VD |
| Dividend (Dv) |
0 <= Dv < S |
Ex-Dividend
Date
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Must be valid dates |
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| To determine the theoretical value of an index option, you
may input the index level for "Stock Price (S)" and strike level for "Strike
Price (X)" accordingly. However, since the maximum value for such field is 20,000, to enter index level higher than 20,000, one may enter, say, 2,010.5 for 20,105. The computed option prices will be the same by simply multiplying the output prices with a factor of 10. |
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| Choose the desired option pricing
model: |
| Binomial: |
Default is American style, may choose European style.
Dividend amount and Ex-Dividend Date may be entered. |
| Black-Scholes: |
European style only. Dividend is ignored. |
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| In general, Binomial Model is used to determine the theoretical
value of stock options while Black-Scholes Model is used to determine the theoretical
value of index options. |
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| Outputs |
| Theoretical Values |
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Both the theoretical values for Calls and Puts will
be computed. |
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Volatility has a significant influence on the price of an option
contract, especially for near-the-money options. Small variations in these estimates
can result in significantly different prices. It is important to understand that
during a trading day the consensus among traders and investors on an estimate
of future market volatility is dynamic, and can change frequently and abruptly.
Transaction costs such as stock borrowing costs are not taken into account during
the computations. Therefore do not expect prices you generate with the calculator
to resemble prices found in the marketplace. |
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| Theoretical Value Matrix |
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A matrix table showing the corresponding theoretical
values for Calls and Puts when the stock price rises or falls by 1%, 2%, 3%,
5% and 10% from the original value are displayed for easy reference. |
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You may make changes to the Strike Price, Expiry Date and/or
Volatility to evaluate the impacts on the theoretical values. Changes to other
parameters such as the Stock Price, Interest Rate and Dividend, and the type
of pricing model used could only be made at the original calculator mode. |
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| Delta |
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A measure of the change in an option value for
a dollar change in the underlying stock price. Call options have positive deltas
as the call value increases as the stock price increases, it ranges from 0 to
1. Put options have negative deltas as the put value declines as the stock price
increases, it ranges from –1 to 0. At-the-money calls have delta values close
to 0.5, while at-the-money puts have delta values close to –0.5.
e.g. If delta of Call ABC June 200 = 0.5, it means that one dollar increase
in the ABC stock price will result in an $0.50 gain in the option value.
Please note that the delta value is only valid for an infinitesimal change
in the underlying stock price, therefore it should not be used to estimate the
change in option value for significant changes in stock prices.
Delta is also referred to as the hedging ratio. An option with a delta of
0.5 will be able to hedge 0.5 lot of the underlying stock (assuming with the
same number of shares per lot), or two option contracts for one lot of stock. |
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| Theta |
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A measure of the change in an option’s theoretical
value for a pre-defined period closer to expiry. The pre-defined period for the
Calculator is 7 days.
e.g. A theta value of –0.3525 implies a decrease of $0.3525 in the option premium
for 7 days closer to expiry. |
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| Gamma |
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A measure of the change in an option delta for
one dollar change in the underlying stock price. The gamma value changes significantly
when the option is near-the-money, hence it is an important parameter during
hedging.
e.g. If the gamma of Call ABC Jan 40 = 0.04, it implies that one dollar increase
(decrease) in ABC share price will result in 0.04 increase (decrease) in the
delta value of the option series. |
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| Implied Volatility refers to the theoretical volatility value
derived from an option pricing model, with inputs of the market value of option
premium and other factors affecting option prices. For equity derivatives of
similar nature to an option, implied volatility reflects the expensiveness of
the product amongst others, assuming all other factors being equal. |
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| Inputs |
| INPUTS |
ACCEPTABLE
RANGES |
| Stock Price (S) |
0 < S < 20,000 |
| Strike Price (X) |
0 < X < 20,000 |
| Interest Rate (R) |
0% < R < 200% |
| Value Date (VD) |
Must be valid dates |
| Expiry Date (ED) |
ED >= VD |
| Dividend (Dv) |
0 <= Dv < S |
Ex-Dividend
Date
|
Must be valid dates |
| Market Price - Call (CP) |
Max [S-Xe-RT, 0.01] < CP < S |
| Market Price - Put (PP) |
Max [X-S, 0.01] < PP < Xe-RT |
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(Where Xe-RT is the present value of the Strike
Price. Market Prices for Call or Put may be entered individually or simultaneously.)
To determine the implied volatility of an index option, you may input the
index level for "Stock Price (S)" and strike level for "Strike
Price (X)" accordingly. However, since the maximum value for such field is 20,000, to enter index level higher than 20,000, one may enter, say, 2,010.5 for 20,105. The market prices for call and put to be entered should be adjusted accordingly. The implied volatility computed will then be the same. |
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| Choose the desired option pricing
model: |
| Binomial: |
Default is American style, may choose European style.
Dividend amount and Ex-Dividend Date may be entered. |
| Black-Scholes: |
European style only. Dividend is ignored. |
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| Outputs |
| Implied Volatility |
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Implied volatility for call or put may be computed
individually or simultaneously. The values for implied volatility are determined
by iterations. It is the volatility that arrives at the Market Price being entered
under the option pricing model. When any of the values computed are either below
zero or above 500, "n.a." will be displayed. |
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