4 ms·

it is used everywhere as the foundation, all the more recent models (stochastic vol/Heston, Local volatility, SABR, SLV, SVI etc) are just incremental extension

it is used everywhere as the foundation, all the more recent models (stochastic vol/Heston, Local volatility, SABR, SLV, SVI etc) are just incremental extensions and generalization of Black-Scholes

dragontamer 7y ago
At its core, Black Scholes is a set of "obvious" differential equations. You assume a normal curve. You define "volatility" (the market's uncertainty to the price of something) as Geometric Brownian motion with some standard-deviation / variance, and then perform differential equations on that to determine the "proper price" of an option. After all: Options grow more valuable in times of uncertainty, and grow less valuable when everyone can accurately predict future prices. The part that "brakes" because of negative rates is the "risk free rate", predicting the future value of money. To me, it seems like there are a variety of obvious extensions you can do to fix this problem. You could redefine Black-Scholes to operate on "Real" terms, and then convert everything back into "normal" terms later. ---------- Black Scholes doesn't "fundamentally" require postivie interest rates for the risk-free rate. It was just an assumption that they had in the original model. But as a differential equation, its pretty easy to tweak your assumptions around and fix these issues. But any such tweak means you're no longer working with classic Textbook Black Scholes. Sure, it served as the basis of the theory, but you gotta account for more real-world variables than the original textbook model.
- Xcelerate 7y ago
  > At its core, Black Scholes is a set of "obvious" differential equations. Interestingly, the Schrodinger equation works about the same way. Just assume a handful of reasonable and "obvious" things about physics, and out pops the equation.
mcguire 7y ago
Isn't Black-Scholes based on a normal distribution? Is that an appropriate probability distribution?

it is used everywhere as the foundation, all the more recent models (stochastic vol/Heston, Local volatility, SABR, SLV, SVI etc) are just incremental extensions and generalization of Black-Scholes

dragontamer 7y ago

At its core, Black Scholes is a set of "obvious" differential equations. You assume a normal curve. You define "volatility" (the market's uncertainty to the price of something) as Geometric Brownian motion with some standard-deviation / variance, and then perform differential equations on that to determine the "proper price" of an option. After all: Options grow more valuable in times of uncertainty, and grow less valuable when everyone can accurately predict future prices. The part that "brakes" because of negative rates is the "risk free rate", predicting the future value of money. To me, it seems like there are a variety of obvious extensions you can do to fix this problem. You could redefine Black-Scholes to operate on "Real" terms, and then convert everything back into "normal" terms later. ---------- Black Scholes doesn't "fundamentally" require postivie interest rates for the risk-free rate. It was just an assumption that they had in the original model. But as a differential equation, its pretty easy to tweak your assumptions around and fix these issues. But any such tweak means you're no longer working with classic Textbook Black Scholes. Sure, it served as the basis of the theory, but you gotta account for more real-world variables than the original textbook model.

Xcelerate 7y ago
> At its core, Black Scholes is a set of "obvious" differential equations. Interestingly, the Schrodinger equation works about the same way. Just assume a handful of reasonable and "obvious" things about physics, and out pops the equation.

mcguire 7y ago

Isn't Black-Scholes based on a normal distribution? Is that an appropriate probability distribution?