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
  

See Also

blkprice, blsprice

References

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

Hull, Options, Futures, and Other Derivative Securities, 2nd edition, Chapter 14.

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