2012 Practice P2.M2_1-20_v3_1112 Mock Exam B Q. 39.8.1

[Jhamby]

I know it is getting a little late to ask these questions. However, I am confused about the formula for d1 vs d2.

In the spreadsheet solution provide for Option pricing model to solve for value of debt & equity, the formula for d1 was given as below (bolded).
Face value of debt $10.000
PV of debt at riskfree $9.608 =E35*EXP(-E10*E11)
d1 $2.327 =(LN(E4/E35)+(E10+E15^2/2)*E11)/(E15*SQRT(E11))

In the Part II FormulaSheet_P2_v3.pdf, it provides the same formula but for d2.

Please note this is the same Black-Scholes Merton option pricing model that is reviewed in
the Hull assignment; merely the notation is different. Specifically, k = d2.

So it looks like the same formula, but one is d1 and the other is d2. What am I missing?

Thanks.

Jim

 

[Jhamby]

I think I just saw the difference. In the second term in the numerator, the risk free rate has one half the variance of assets subtracted from it to calc d2. In d1 that same term is added to the risk free rate.

Nevertheless, some instruction on when to use which would be helpful. Thanks.

 

[ShaktiRathore]

d2=d1-sigma*root(T) so a positive variance in d1 is converted to negative variance in d2. N(d2) gives the probability of asset finishing in the money so N(-d2) gives probability of asset finishing OTM or to assess probability of default,N(d1) is delta of option is term comes with Asset value in black scholes formula.
Thanks

 

[Jhamby]

Thanks.