binprice (Financial Toolbox)

Binomial put and call pricing.

Syntax

[pr, opt] = binprice(so, x, r, t, dt, sig, flag, q, div, exdiv)

Arguments

so: Underlying asset price. A scalar.

x: Option exercise price. A scalar.

r: Risk-free interest rate. A scalar. Enter as a decimal fraction.

t: The option's time until maturity in years. A scalar.

dt: The time increment within t. A scalar. dt is adjusted so that the length of each interval is consistent with the maturity time of the option. (dt is adjusted so that t divided by dt equals an integer number of increments.)

sig: The asset's volatility. A scalar.

flag: Specifies whether the option is a call (flag = 1) or a put (flag = 0). A scalar.

q: The dividend rate, as a decimal fraction. A scalar. Default = 0. If you enter a value for q, set div and exdiv = 0 or do not enter them. If you enter values for div and exdiv, set q = 0.

div: The dividend payment at an ex-dividend date, exdiv. A 1-by-N vector. For each dividend payment, there must be a corresponding ex-dividend date. Default = 0. If you enter values for div and exdiv, set q = 0.

exdiv: Ex-dividend date, specified in number of periods. A 1-by-N vector. Default = 0.

Description

[pr, opt] = binprice(so, x, r, t, dt, sig, flag, q, div, exdiv)

prices an option using a binomial pricing model.

Example

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:

[pr, opt] = 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:

pr =
   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
opt =
    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