blkprice (Financial Toolbox)

Black's option pricing.

Syntax

[call, put] = blkprice(f, x, r, t, sig)

Arguments

f: Forward price of underlying asset at time zero. Must be greater than 0. You can extend Black's model to interest-rate derivatives (call and put options embedded in bonds) by calculating the forward price from the equation

f = (B - I) * exp(r*t)
where B is the face value of the bond and I is the present value of the coupons during the life of the option.
x
Strike or exercise price of the options.  Must be greater than 0.
r
Risk-free interest rate (plus storage costs less any convenience yield).  Must be greater than or equal to 0.
t
Time until maturity of option in years.  Must be greater than 0.
sig
Volatility of the price of the underlying asset.  Must be greater than or equal to 0.

Description

[call, put] = blkprice(f, x, r, t, sig)

uses Black's model to value an option and returns the call and put option prices.

Note: This function uses normcdf, the normal cumulative distribution function in the Statistics Toolbox.

Example

The forward price of a bond is $95, the exercise price of the option is $98, the risk-free interest rate is 11%, the time to maturity of the option is 3 years, and the volatility of the bond price is 2.5%.

[call, put] = blkprice(95, 98, 0.11, 3, 0.025)
call =
    0.4162 (or $0.42)
put =
    2.5729 (or $2.57)

References

Hull, Options, Futures, and Other Derivative Securities, 2nd edition, Formulas 15.7 and 15.8.

Black, "The Pricing of Commodity Contracts," Journal of Financial Economics, March 3, 1976, pp. 167-179.