PROJECT IDEAS
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1. Read and write a simple summary of

IMPLIED BINOMIAL TREES
By:RUBINSTEIN, M (RUBINSTEIN, M)

JOURNAL OF FINANCE

Volume: 49 Issue: 3 Pages: 1094-1095
Published: JUL 1994


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2. Numerically study the mean and variance of hedging outcomes with
different values of volatility.  Use the "simulated prices" Matlab
code.  Which value of volatility produces best results?



PRESENTATION IDEAS
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The task is to prepare a presentation that is either
1. To be delivered in class
or
2. To be posted as video online (sides with a voiceover)
The presentation should be about 15 minutes long.


Possible topics:

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1. Showing that the binomial tree model answer converges to the BS
formula.

Use Cox--Ross--Rubinstein original article
(a)  Cox, J. C.; Ross, S. A.; Rubinstein, M. (1979). 
"Option pricing: A simplified approach". 
Journal of Financial Economics 7 (3): 229. 
doi:10.1016/0304-405X(79)90015-1

and de Moivre--Laplace theorem (or, better, the qualitative bound of
Berry--Esseen), see for example, Chap I, Sec 6.2-3 of A.N.Shiryaev's
"Probability" (any good book on probability would have it)

(b) Shiryaev, A.N.
Probability
Available online through A&M Library
http://link.springer.com/book/10.1007%2F978-1-4757-2539-1

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2. Original derivations of Black--Scholes and Merton
Understand and summarize the original derivations

(a) PRICING OF OPTIONS AND CORPORATE LIABILITIES
By:BLACK, F (BLACK, F); SCHOLES, M (SCHOLES, M)
JOURNAL OF POLITICAL ECONOMY
Volume: 81  Issue: 3  Pages: 637-654
DOI: 10.1086/260062

(b) Merton, Robert. 
"Theory of Rational Option Pricing". 
Bell Journal of Economics and Management Science 4 (1): 141--183. 
doi:10.2307/3003143.

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3. A discussion between Derman--Taleb and Merton's students

(see http://seekingalpha.com/article/113072-taleb-vs-merton-cont for background and rumours)

Compare the papers, summarize their arguments, form and argue your opinion.

(a)
The illusions of dynamic replication
By:Derman, E (Derman, E); Taleb, NN (Taleb, NN)
QUANTITATIVE FINANCE
Volume: 5  Issue: 4  Pages: 323-326
DOI: 10.1080/14697680500305105

(b)
Derman and Taleb's 'The illusions of dynamic replication': a comment
By:Ruffino, D (Ruffino, Doriana); Treussard, J (Treussard, Jonathan)
QUANTITATIVE FINANCE
Volume: 6  Issue: 5  Pages: 365-367
DOI: 10.1080/14697680600868283

both available online at TAMU.

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4. Asset price model: average versus almost sure growth

Discuss the mathematics behind the "paradox" where an individual asset
price will eventually collapse while the average keeps growing.

The article
(a) J.A.D. Appleby, G. Berkolaiko, A. Rodkina, 
Non-exponential stability and decay rates in nonlinear stochastic
difference equation with unbounded noises, 
Stochastics, 81, 99-127 (2009) 
DOI:10.1080/17442500802088541
[ PDF, math.PR/0610425 ].
is much more general than necessary for this question, but at least
written by great people.