Financial Toolbox™

binprice

Binomial put and call pricing

Syntax

[AssetPrice, OptionValue] = binprice(Price, Strike, Rate, Time, 
Increment, Volatility, Flag, DividendRate, Dividend, ExDiv)

Arguments

`Price`	Underlying asset price. A scalar.
`Strike`	Option exercise price. A scalar.
`Rate`	Risk-free interest rate. A scalar. Enter as a decimal fraction.
`Time`	Option's time until maturity in years. A scalar.
`Increment`	Time increment. A scalar. `Increment` is adjusted so that the length of each interval is consistent with the maturity time of the option. (`Increment` is adjusted so that `Time` divided by `Increment` equals an integer number of increments.)
`Volatility`	Asset's volatility. A scalar.
`Flag`	Specifies whether the option is a call (`Flag = 1`) or a put (`Flag = 0`). A scalar.
`DividendRate`	(Optional) The dividend rate, as a decimal fraction. A scalar. Default = 0. If you enter a value for `DividendRate`, set `Dividend` and `ExDiv` = `0` or do not enter them. If you enter values for `Dividend` and `ExDiv`, set `DividendRate` = `0`.
`Dividend`	(Optional) The dividend payment at an ex-dividend date, `ExDiv`. A row vector. For each dividend payment, there must be a corresponding ex-dividend date. Default = 0. If you enter values for `Dividend` and `ExDiv`, set `DividendRate` = `0`.
`ExDiv`	(Optional) Ex-dividend date, specified in number of periods. A row vector. Default = 0.

Description

[AssetPrice, OptionValue] = binprice(Price, Strike, Rate, Time, Increment, Volatility, Flag, DividendRate, Dividend, ExDiv) prices an option using the Cox-Ross-Rubinstein binomial pricing model.

Examples

For a put option, the asset price is $52, option exercise price is $50, risk-free interest rate is 10%, option matures in 5 months, volatility is 40%, and there is one dividend payment of $2.06 in 3-1/2 months.

[Price, Option] = binprice(52, 50, 0.1, 5/12, 1/12, 0.4, 0, 0,... 
2.06, 3.5)

returns the asset price and option value at each node of the binary tree.

Price =

   52.0000   58.1367   65.0226   72.7494   79.3515   89.0642
         0   46.5642   52.0336   58.1706   62.9882   70.6980
         0         0   41.7231   46.5981   49.9992   56.1192
         0         0         0   37.4120   39.6887   44.5467
         0         0         0         0   31.5044   35.3606
         0         0         0         0         0   28.0688
Option =

    4.4404    2.1627    0.6361         0         0         0
         0    6.8611    3.7715    1.3018         0         0
         0         0   10.1591    6.3785    2.6645         0
         0         0         0   14.2245   10.3113    5.4533
         0         0         0         0   18.4956   14.6394
         0         0         0         0         0   21.9312

References

Cox, J., S. Ross, and M. Rubenstein, "Option Pricing: A Simplified Approach", Journal of Financial Economics 7, Sept. 1979, pp. 229-263.