BinomialAmerican
Updated: 04 Sep 2012
Use BinomialAmerican to calculate the price, delta, gamma, theta, vega, rho, or lambda of an American option using the Binomial Tree option pricing formula.
Syntax
SELECT [wctOptions].[wct].[BinomialAmerican] (
<@CallPut, nvarchar(4000),>
,<@AssetPrice, float,>
,<@StrikePrice, float,>
,<@TimeToMaturity, float,>
,<@RiskFreeRate, float,>
,<@DividendRate, float,>
,<@Volatility, float,>
,<@NSteps, int,>
,<@ReturnValue, nvarchar(4000),>)
Arguments
@CallPut
identifies the option as being a call ('C') or a put ('P'). @CallPut is an expression of type nvarchar or of a type that can be implicitly converted to nvarchar.
@AssetPrice
the price of the underlying asset. @AssetPrice is an expression of type float or of a type that can be implicitly converted to float.
@StrikePrice
the exercise price of the option. @StrikePrice is an expression of type float or of a type that can be implicitly converted to float.
@TimeToMaturity
the time to expiration of the option, expressed in years. @TimeToMaturity is an expression of type float or of a type that can be implicitly converted to float.
@RiskFreeRate
the annualized, continuously compounded risk-free rate of return over the life of the option. @RiskFreeRate is an expression of type float or of a type that can be implicitly converted to float.
@DividendRate
the annualized, continuously compounded dividend rate over the life of the option. For currency options, @DividendRate should be the foreign risk-free interest rate. @DividendRate is an expression of type float or of a type that can be implicitly converted to float.
@Volatility
the volatility of the relative price change of the underlying asset. @Volatility is an expression of type float or of a type that can be implicitly converted to float.
@nSteps
the number of steps in the binomial tree. @nSteps is an expression of type int or of a type that can be implicitly converted to int.
@ReturnValue
identifies the calculation to be performed. @ReturnValue is an expression of type nvarchar or of a type that can be implicitly converted to nvarchar. @ReturnValue is not case-sensitive. The following values are acceptable for @ReturnValue.
|
@ReturnValue
|
Returns
|
|
'P', 'PRICE'
|
Price
|
|
'D', 'DELTA'
|
Delta
|
|
'G', 'GAMMA'
|
Gamma
|
|
'V', 'VEGA'
|
Vega
|
|
'T', 'THETA'
|
Theta
|
|
'R', 'RHO'
|
Rho
|
|
'L', 'LAMBDA'
|
Lambda
|
Return Type
float
Remarks
· @Volatility must be greater than zero (@Volatility > 0).
· @TimeToMaturity must be greater than zero (@TimeToMaturity > 0).
· @AssetPrice must be greater than zero (@AssetPrice > 0).
· @StrikePrice must be greater than zero (@StrikePrice > 0).
· @nSteps must be greater than 1 (@nSteps > 1)
· If @ReturnValue is NULL, then @ReturnValue is set to 'P'.
· If @DividendRate is NULL an error will be returned
· If @RiskFreeRate is NULL an error will be returned
Example
Calculate the price for a call option on 2012-09-04, expiring on 2012-12-15, with a current asset price of 99.5, a strike price of 100 and a volatility of 20%. The risk free rate is 2% and the dividend rate is 0.5%. The number of steps is 100.
SELECT cast(wct.BinomialAmerican(
'C' --PutCall
,99.5 --Asset Price
,100 --Strike Price
,datediff(d,'2012-09-04','2012-12-15') / 365.0000 --Time-to-expiry
,.02 --Risk Free Rate
,.005 --Dividend Rate
,.20 --Volatility
,100 --Number of Steps
,NULL --Return Value
) as money) as Price
This produces the following result.
Price
---------------------
4.1547
To calculate the delta for the same option:
SELECT cast(wct.BinomialAmerican(
'C' --PutCall
,99.5 --Asset Price
,100 --Strike Price
,datediff(d,'2012-09-04','2012-12-15') / 365.0000 --Time-to-expiry
,.02 --Risk Free Rate
,.005 --Dividend Rate
,.20 --Volatility
,100 --Number of Steps
,'D' --Return Value
) as money) as Delta
This produces the following result.
Delta
---------------------
0.5172
In this example we calculate the Call and Put prices for the same option with a series of different asset prices.
SELECT cast(n.S as money) as [Underlying]
,cast(wct.BinomialAmerican(
'C' --PutCall
,n.s --Asset Price
,100 --Strike Price
,datediff(d,'2012-09-04','2012-12-15') / 365.0000 --Time-to-expiry
,.02 --Risk Free Rate
,.005 --Dividend Rate
,.20 --Volatility
,100 --Number of Steps
,'P' --Return Value
) as money) as [Call Price]
,cast(wct.BinomialAmerican(
'P' --PutCall
,n.s --Asset Price
,100 --Strike Price
,datediff(d,'2012-09-04','2012-12-15') / 365.0000 --Time-to-expiry
,.02 --Risk Free Rate
,.005 --Dividend Rate
,.20 --Volatility
,100 --Number of Steps
,'P' --Return Value
) as money) as [Put Price]
FROM (
SELECT 98.5 UNION ALL
SELECT 99.0 UNION ALL
SELECT 99.5 UNION ALL
SELECT 100 UNION ALL
SELECT 100.5 UNION ALL
SELECT 101
) n(S)
This produces the following result.
Underlying Call Price Put Price
--------------------- --------------------- ---------------------
98.50 3.6582 4.7761
99.00 3.9064 4.5225
99.50 4.1547 4.2696
100.00 4.4029 4.0171
100.50 4.6907 3.8013
101.00 4.9785 3.5878