"Beyond Black-Scholes: On L evy-Stable Models for Valuation of Generalized Financial Instruments"
by D. L. Hall, V. E. Hemming, and G. Lambeau
As part of the movie, Vince reviews a paper he wrote with his old friend Dave Hall and his advisor at MIT, Prof. Lambeau (yes, the Fields Medalist from "Good Will Hunting). Apparently, Mark and Dave were mutual friends of "Raging" Dave Hall.
Monday, April 15, 2013
Wednesday, April 3, 2013
Audition Schedule
Unitarian Universalist Church
147 High St., Medford, MA
3/6/13 (1 PM - 5 PM)
1 PM: Setup and Lunch.
1:15 PM: Introduction (Jim Kelly). Introduce crew and characters.
1:30 PM - 2:30 PM: Audition (1)
2:30 PM - 2:45 PM: Break.
2:45 PM - 3:45 PM: Audition (2)
3:45 PM - 4:00 PM: Break
4:00 PM - 4:45 PM: Audition (3)
4:45 PM - 5:00 PM: Closing Remarks (Jim Kelly) and Break-Down.
Unitarian Universalist Church
147 High St., Medford, MA
3/6/13 (1 PM - 5 PM)
1 PM: Setup and Lunch.
1:15 PM: Introduction (Jim Kelly). Introduce crew and characters.
1:30 PM - 2:30 PM: Audition (1)
2:30 PM - 2:45 PM: Break.
2:45 PM - 3:45 PM: Audition (2)
3:45 PM - 4:00 PM: Break
4:00 PM - 4:45 PM: Audition (3)
4:45 PM - 5:00 PM: Closing Remarks (Jim Kelly) and Break-Down.
- Please choose a time-block to audition.
- We'll have a sign-in sheet when you arrive.
Tuesday, April 2, 2013
What is a "Quant"?
Both Vince and Mark are quantitative analysts, or "quants". Quants typically study math, physics, or the more theoretical areas of engineering (for instance, aeronautical engineering). Back in the late 80's, there were too many physics and applied math Ph.D.'s and not enough jobs; at the same time, Wall Street was looking to develop numerical models for pricing derivatives and other financial instruments. Rather than drift from postdoc to postdoc, lots of Ph.D.'s joined the dark side as quants.
http://www.nytimes.com/2009/03/10/science/10quant.html?pagewanted=all&_r
The bedrock of derivative models is Black-Scholes, which is a stochastic partial differential equation that allows a valued to be assigned to a call option. Let's define each term.
A call option is a contract that allows the owner to buy a stock (or some other instrument) at a given price (a strike price). An option consists of two terms: 1) the extrinsic value, which is the difference between the stock price and the strike price, and 2) the intrinsic value, which depends on both the volatility of the stock and the expiration date. 1) is trivial to calculate, whereas 2) requires a model for how the stock price fluctuates. The Black-Scholes model assumes the stock price fluctuates according to a Gaussian distribution; this fluctuation is analogous to the random motion of a gas and is called Brownian Motion (Albert Einstein wrote his Ph.D. thesis on Brownian motion). This random motion is called a random processes and is part of the toolkit of any physicist or applied mathematician. The Black-Scholes model gives an equation which relates the change in the derivative value with respect to the change in the stock value. We can then solve (either on paper or using a computer) this equation, and calculate the derivative value given the stock value.
But stock prices don't behave like gas molecules. They are subject to external shocks. They are subject to discontinuities. Brownian motion is continuous everywhere, and hence does not model this behavior. What we need is a random motion with jumps, or infinite variance. A very large class of random variables that exhibit these jumps are called Levy Stable.
https://en.wikipedia.org/wiki/Stable_distribution
These distributions obey a generalized central limit theorem, which states that a Levy stable distribution is the limiting distribution of a large number of independent, identically distributed (IID) random variables with possibly infinite variance. The resulting motion is discontinuous, like the stock price of Lehman Brothers in September of 2008
Both Vince and Mark are quantitative analysts, or "quants". Quants typically study math, physics, or the more theoretical areas of engineering (for instance, aeronautical engineering). Back in the late 80's, there were too many physics and applied math Ph.D.'s and not enough jobs; at the same time, Wall Street was looking to develop numerical models for pricing derivatives and other financial instruments. Rather than drift from postdoc to postdoc, lots of Ph.D.'s joined the dark side as quants.
http://www.nytimes.com/2009/03/10/science/10quant.html?pagewanted=all&_r
The bedrock of derivative models is Black-Scholes, which is a stochastic partial differential equation that allows a valued to be assigned to a call option. Let's define each term.
A call option is a contract that allows the owner to buy a stock (or some other instrument) at a given price (a strike price). An option consists of two terms: 1) the extrinsic value, which is the difference between the stock price and the strike price, and 2) the intrinsic value, which depends on both the volatility of the stock and the expiration date. 1) is trivial to calculate, whereas 2) requires a model for how the stock price fluctuates. The Black-Scholes model assumes the stock price fluctuates according to a Gaussian distribution; this fluctuation is analogous to the random motion of a gas and is called Brownian Motion (Albert Einstein wrote his Ph.D. thesis on Brownian motion). This random motion is called a random processes and is part of the toolkit of any physicist or applied mathematician. The Black-Scholes model gives an equation which relates the change in the derivative value with respect to the change in the stock value. We can then solve (either on paper or using a computer) this equation, and calculate the derivative value given the stock value.
But stock prices don't behave like gas molecules. They are subject to external shocks. They are subject to discontinuities. Brownian motion is continuous everywhere, and hence does not model this behavior. What we need is a random motion with jumps, or infinite variance. A very large class of random variables that exhibit these jumps are called Levy Stable.
https://en.wikipedia.org/wiki/Stable_distribution
These distributions obey a generalized central limit theorem, which states that a Levy stable distribution is the limiting distribution of a large number of independent, identically distributed (IID) random variables with possibly infinite variance. The resulting motion is discontinuous, like the stock price of Lehman Brothers in September of 2008
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