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Evaluation services of Stock Option
Selection of evaluation models and implementation of parameters are based on the issuance conditions of stock options.
As it is necessary to carry out evaluation that is most appropriate for the issuance conditions,
the flow for calculation is as follows.
Our company can respond to the calculation by all models according to the purpose of stock option valuation.
①Preparation and selection of evaluation models according to the issuance conditions
Stock option valuation is mainly conducted by the following three methods.
- Black-Scholes Model
- Lattice Model
- Simulation Model
Black-Scholes Model
Since the Black-Scholes Model is a model which evaluates a European option (option transaction which can exercise a right only on the maturity date),
it is not premised on evaluating an American option (option transaction which can be exercised at any time).
To be exact, although the Black-Scholes Model can assist the evaluation of an American option in scenarios
such as using the Monte Carlo simulation, the model itself cannot evaluate an Amercian option.
The calculating formula is listed as follows. Besides,
the calculating formula of the Black-Scholes Model
is also published on our website. A rough estimated value can be otained before committing for a real evaluation.
Calculating formula
Lattice Model
Binomial Model and Tinomial Model are the representatives of the Lattice Model.
They subdivide and analyze the pattern of change in stock price from a certain point of time,
which allows projection of more precise result of complicated calculations than the Black-Scholes model.
Since the Lattice Model subdivides the whole exercise period and compares the strike price and the option price,
it allows evaluation of American options (option transaction which can be exercised at any time) and calculation of complicated options.
The calculation formula is shown below. This is a method of calculating option value based on the change of stock price,
assuming that the change of stock price follows the lattice pattern.
Calculating formula
This model divides an option till its maturity into several fixed periods and shows the transition of stock price by making use of many lattices. The number of partitions of the period is called Node and theoretically the larger the number, the more accurate evaluation can be achieved.
As a method of concrete simulation, the flow is listed as followed.
- To prepare the transition of stock price until the maturity date
- To calculate option value at maturity (UL-K) by using the prepared stock prices
- To compare the discounted values (the expected values) of option value (UL-K) at each calculation point (i) and that after one period (i+1) and take the larger one as
- To calculate option value of the whole period from the very first beginning
When we calculate option value here, the expected value is computed by using the rise and fall probability. This probability is called risk neutral probability. Although a detailed explanation is not given here, it is assumed that the expected value of the rise and fall of stock price equals to the earning rate (return) of risk-free assets.
Simulation Model
Option value is calculated by using the Monte Carlo simulation.
Even stock options with complicated conditions can be evaluated depending on the settings of Simulation Model.
Other conditions
Although the main evaluation methods are stated as above, under real circumstances, there is possibility that general evaluation models are not applicable and that unique evaluation model has to be created.
- Exercise period (exercise start date and exercise end date)
- Timing of exercise (at maturity only, monthly, or at any time)
- Kind of strike price (constant and floating)
- Presence of upper and lower limits of strike price
When the exercise start date is later than the issuance date of stock acquisition rights (stock option),
it becomes a postdated transaction (forward contract). Since postdated transaction itself is a derivative,
when making evaluation, adjustment of the periods stating the possibility of exercise is needed.
As mentioned above, the Black-Scholes Model cannot be used at the time of exercising, except for the exercise end time.
In addition, adjustment of the model becomes necessary depending on the timing of the exercise.
In the case of an option with exercise amendment right represented by MSCB (moving strike),
adjustment of the model also becomes necessary.
Furthermore, adjustment of the model is necessary when the upper limit value and the bottom value are set when the strike price changes.
②Presumption of the parameter used for evaluation
Basically, the following items should be noted when presuming the parameter.- Thorough presumption of volatility in the case where past stock prices do not exist
- Dilution estimates of future dividends
- Setting of term structure
- Necessity of setting volatility smile (skew) by derivation of the strike price and stock price
Volatility is the most important parameter that should be considered when obtaining option value.
Since option value increases when volatility grows (please refer to the explanation after next page for details),
it is necessary to decide the numerical value of volatility carefully.
The next influencing item is the dividend rate.
It affects the change of stock price by the expiration of right when dividend is being paid.
Since option value falls when dividend rate increases, it is a critical factor affecting the option value.
③Calculation of option value
It is a step to use the calculation model parameter determined in ① and ② to compute calculation.
Regarding the Black-Scholes model, since our website contains calculating formula of the Black-Scholes model, please feel free to use it for rough calculation before committing the actual evaluation.
Please read the following file for details.
Introduction of stock option valuation services（PDF）
For details of the contents and amount of valuation, please click here to contact us.
Moreover, please view the following site to learn more about stock option valuation.
