blkprice (Financial Toolbox)

Black's option pricing

Syntax

[Call, Put] = blkprice(ForwardPrice, Strike, Rate, Time, Volatility)

Arguments

ForwardPrice
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, I is the present value of the coupons during the life of the option, r is the risk-free interest rate, and t is the time until maturity.

Strike
Strike or exercise price of the options. Must be greater than 0.

Rate
Risk-free interest rate (plus storage costs less any convenience yield). Must be greater than or equal to 0.

Time
Time until maturity of option in years. Must be greater than 0.

Volatility
Volatility of the price of the underlying asset. Must be greater than or equal to 0.

`ForwardPrice`	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, `I` is the present value of the coupons during the life of the option, `r` is the risk-free interest rate, and `t` is the time until maturity.
`Strike`	Strike or exercise price of the options. Must be greater than 0.
`Rate`	Risk-free interest rate (plus storage costs less any convenience yield). Must be greater than or equal to 0.
`Time`	Time until maturity of option in years. Must be greater than 0.
`Volatility`	Volatility of the price of the underlying asset. Must be greater than or equal to 0.

Description

[Call, Put] = blkprice(ForwardPrice, Strike, Rate, Time, Volatility) 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.

Examples

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)

See Also

binprice, blsprice

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.

blkimpv blsdelta