Financial Toolbox |
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blkprice
Black's option pricing
Syntax
[Call, Put] = blkprice(ForwardPrice, Strike, Rate, Time, Volatility)
Arguments
ForwardPrice
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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.
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Strike
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Strike or exercise price of the options. Must be greater than 0.
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Rate
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Risk-free interest rate (plus storage costs less any convenience yield). Must be greater than or equal to 0.
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Time
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Time until maturity of option in years. Must be greater than 0.
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Volatility
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Volatility of the price of the underlying asset. Must be greater than or equal to 0.
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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.
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 |  |