Geometric Brownian Motion and Black Scholes Formulas

Discussion in 'P1.T2. Quantitative Methods (20%)' started by intuit2k2, Nov 18, 2010.

1. intuit2k2New Member

Are we expected to know the formulas for GMB and BScholes (including d1 and d2). Should we expect simple pricing questions and calculating St based on mean, St-1 and sigma?

2. David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Technically yes, per AIMs:
Hull Chapter 13
"• Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected return.
• Compute the realized return and historical volatility of a stock.
• List and describe the assumptions underlying the Black-Scholes-Merton option pricing model.
• Compute the value of a European option using the Black-Scholes-Merton model on a non-dividend-paying stock."

But it's hard to say for BSM b/c they have to give you N(.).
My videos, for a while, have emphasized the importance of d2 (the probability of the option will expire ITM):
[LN(S/K) + (r - sigma^2/2)T]/(sigma*SQRT[T])
... because if you replace (r) with asset return, you've got Merton's distance to default (DD)

David

3. intuit2k2New Member

I didn't think we had to know the Merton model - is this for level 2?

4. David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Yes, Merton is in credit risk (topic 6) ... IMO, making the association is still productive

5. Jiew KwangMember

Technically yes, per AIMs:
Hull Chapter 13
"• Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected return.
• Compute the realized return and historical volatility of a stock.
• List and describe the assumptions underlying the Black-Scholes-Merton option pricing model.
• Compute the value of a European option using the Black-Scholes-Merton model on a non-dividend-paying stock."

But it's hard to say for BSM b/c they have to give you N(.).
My videos, for a while, have emphasized the importance of d2 (the probability of the option will expire ITM):
[LN(S/K) + (r - sigma^2/2)T]/(sigma*SQRT[T])
... because if you replace (r) with asset return, you've got Merton's distance to default (DD)

David​

Hi David,

You mentioned that the d2 is the probability of the option expiring ITM. What about d1?

Thanks!