Use

The market price calculator for stock options calculates current market values, time values, and future market values (the future point in time is the horizon).

Options on stocks have two variants, call and put. Both the American and the European exercise possibilities are available. The buyer has the right to either buy (call) or sell (put) a stock on a particular date (when exercised according to European standards), or during a specified period (according to American standards), at an agreed-upon price (strike price).

When valuing an option, the theoretical price of the option on the horizon is determined. In addition to the forward price of the stock class from the horizon (spot rate), several other items go into the option formulae (Black-Scholes formula for European options, binomial tree for American). The other items are the strike price, the validity period, the risk-free interest rate on the horizon, and the price volatility of the stock. The calculation assumes 30 or 31 periods. The user needs to predetermine the price volatility of the stock.

As the future stock price on the horizon is not known, it has to be determined in terms of arbitrage. You want to have the stock as a position on the horizon. To achieve this, you can either use the price of the stock on the evaluation date and hold it until the horizon (and also the dividend payments), or you can call the stock on the horizon at the forward price. The latter allows you to invest an amount on the evaluation date, which gathers interest at the risk-free rate until the expiration date. Since both transactions have the same value based on assumption of being free of arbitrage, the forward price is the one on the horizon. Our current release does not calculate the forward price. Instead it is easier to use the current price.

Integration / Calculation Basis

In order to value share options, you need the transaction data, and alternatively a par coupon or zero coupon yield curve in the transaction currency for the evaluation date.

For valuing options, you also need the relevant price volatility for the stock class, and the stock price.

The following input parameters are calculated, which later go into the option price formula:

A spot is the valid price of a stock class in the transaction currency (in the current release this means the current price).

If a price volatility curve is available, then the volatility which goes into the option price formula is the one from the curve with a validity period the same as the one of the option.

Zero bond discounting factors are calculated from the yield curve of the transaction currency. These, along with zero interest rates, can potentially be used for determining risk-free interest rates at a later date.

You can use the zero coupon calculation method for this.

If the transaction currency differs from the display currency of the option, the transaction currency is changed into the display currency using the currency rate from the horizon. If the horizon is later than the evaluation date, the corresponding forward currency rate is calculated for the evaluation date using the yield curves from the transaction and display currencies.

The following function modules, among other things, are used in calculating the input parameters:

Scope of Functions / Valuation

The option price calculator for valuing European options and the one for valuing American ones (using the binomial tree) use the following parameters:

As a result, you get the simulated and standardized value of the option on the horizon (BW ₁ ). The NPV is then the calculated option price multiplied by the number of stocks (ST) the option is based on.

Along with the symbols given already, the following are also used:

NPV = KBWST

where:

If the display currency differs from the transaction currency, the NPV is calculated using the forward currency rate.