VanillaOptions : theta from ql vs other pricers

[iosif ziman]

I am looking at matching greeks between quantlib and alternative pricers. I found that I manage to match delta, gamma, vega, rho but NOT theta. I am using GeneralizedBlackScholes.

The Bloomberg OV pricer gives me -8.87 for data below. With ql I have abt -37

I tried different daycount convenctions including Actual 365 (Fixed) and Business252. Any idea what may I be missing.

today's date 1 Mar 2010
set global evaluation date TRUE
       
settlement date 3 Mar 2010
calendar Target
volatility 0.40
day counter Business252
       
underlying 11543.73
risk free rate 0.08
dividend yield 0.00
       
exercise date 30 Mar 2010
       
payoff type Vanilla
option type CALL
strike 11800.00
       
NPV 419.95
gamma 0.000313585
vega 12.58999954
theta -37.05396289
rho 3.710256838

[Ferdinando M. Ametrano-3]

On Mon, Mar 1, 2010 at 10:50 AM, iosif ziman <[hidden email]> wrote:

> I am looking at matching greeks between quantlib and alternative pricers. I

> found that I manage to match delta, gamma, vega, rho but NOT theta.

mmm... if you match value, delta, and gamma then theta is fixed by Black-Scholes equation...

with your data this is what I get (see the attached QLXL spreadsheet)

TimeToExpiry 0.0740

vol         40.00%

RiskFreeRate 8.0000%

DividendRate 0.0000%

Spot         11543.73

Strike         11800.00

Value 416.97

Delta 0.46294

Gamma 0.00032

Theta -3766.04

in the spreadsheet I've replicated that Theta value using both Black/Scholes and numerically by finite differences, so it's correct

Beware that different definition of Theta are available, the one I'm referring to is the derivative of value with respect to time with inverted sign (and so it depends on how you measure time). Another common definition is ThetaPerDay = Theta/365

ciao -- Nando

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