Geometric Brownian Motion and Black Scholes Formulas
- Thread starter intuit2k2
- Start date
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
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
Yes, Merton is in credit risk (topic 6) ... IMO, making the association is still productive
Jiew Kwang
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
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!
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