## Verifying given numbers in Example 4.1

This forum is to discuss the book "the concepts and practice of mathematical finance" by Mark Joshi.

### Verifying given numbers in Example 4.1

Hello,

I was working through Example 4.1 and I decided to verify the given numbers. For some reason, I was not able to verify Delta for the digital put. I went and derived the corresponding formulas for a digital put under the Black-Scholes model. I hope these are accurate:

price = e^{-rt} (1-N(d_2))
Delta = -e^{-rt} N'(d_2) / (S sigma sqrt(t))
Gamma = e^{-rt} N'(d_2) d_1 / (S^2 sigma^2 t)
Vega = exp{-rt} N'(d_2) d_1 / sigma.

In any case, I plugged the numbers in and got, for option A,

price = 0.310
Delta = -0.037901
Gamma = 0.002
Vega = 1.886

The discrepancy in Delta seems too big to be merely rounding, or what have you. If anyone out there could be kind enough to help me resolve this I would be much obliged. Thanks!
wannabe quant

Posts: 1
Joined: Sat Jul 02, 2011 2:18 am

### Re: Verifying given numbers in Example 4.1

my pricer definitely gives

-0.034294386
mj