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International markets and foreign exchange operations - Savluk M.І.

14.3. Prize Options

For a premium prize option, the Black-Scholes model is victorious. There’s a lot of trust for the European options call on shares, for which you don’t pay dividends until the date of the option. Potimo it’s shown that the model is valid for the American option call without paying dividends.

Another shortcoming of the cob model is the stiffness of the shares until the dividend without dividends - the increase in the number of the added multiplier. Poton won the Bula is broadened by the first prize of the option for the active.

The Black-Scholes formula for call options on shares without dividends. Vart_ option call be identified by the formula




- line-based price of the underlying asset;

- The price of the viscous option;

- Richna rate narahuvannya vidotsotka on assets without rziziku, aka narakhovuetsya without interruption;

- an hour before the end of the option in parts of the rock (a , de t is the number of days, which are left until the end to the option);

? - Risik of the underlying asset (standardly vіdkhilennya dіhіdnostі of the underlying asset for rіk);

- the function of cumulative normal distribution with a mean of 0 and a standard view of 1 (tabulated in the statistics of functions).

Zauvazhimo, scho pid hour of uninterrupted narahuvannya vidotsotka vikoristovuetsya formula maybutnyo vartostі de F - maybutnya vartіst, P - threaded wartіst . In addition to the rate of continuous interruption of R and the rate of simple movement r існує such a sound: . Tsey zv'yazok let’s simplify the Black-Scholes formula.

A formula has been shown to show the nature of the occurrence price of the call option call of the official:

  • Chim vishcha price of the underlying asset, Tim vishta vart_st option;
  • Chim Vishna Tsіna Vikonannya, Tim Nizhcha Tsіna Optsionu;
  • chim more than an hour before the date of marriage, tim vishcha price opt_ionu;
  • Chim vishcha rate without riziku, Tim bіlsha tsina optsіonu;
  • what is the greatest risik (volatility) of the underlying asset, what is the price of options.

Formula parity opt_ion_v call i put. Існу ц formula parity price, why yes I can help you for the guaranteed price option call call value price option put

de - price option put.

Modification formula for shares with dividends. As a rule, the rate of dividends is paid at the top, so you have to pay up to the date of closing the option, then you can take a look at it as a percentage, you can go on and on. For the first time, the formula for premium call option on dividends has been modified:

de - the interest rate, which is guaranteed to be uninterruptedly and that is the dividend rate on the share.

The parity formula is optional:

Establishment of a formula for greater assets. The premium on regional option calls to pay for one of the hint formulas is fallow, in addition to the period of coupon payment, no way. For the umpteenth time, Q is the interest rate, which can be replenished uninterruptedly and always in the form of coupon income.

The stock exchange Yandex looks like a stock with a premium rate. Dividend on Yandex to respect the middle price for the capitalized rate of the higher dividends of the share company, which is included before the index. Q - the rate is always unlimited.

I look at foreign currency as a stock with a different rate of dividends (for such a rate, take the rate of the most profitable rate without the risk of higher currencies).

Zauvazhimo, the Black-Scholes formula is unapproachable for rose-based calculators. For the price tag, special programs are optional calculators.