This course focuses on the traditional models that are currently adopted to specify the fair prices of financial assets under no arbitrage condition. The range of assets is from the single stock or bond to complex derivatives. Different frameworks are examined depending on the characterization of time and/or uncertainty. The question of pricing crypto-assets is also addressed. The course will be developed in tight relation to Financial Econometrics and Quantitative methods in finance courses.

1 Stock pricing: Random Walk and Present Value Model (1 session)

Efficient Market Hypothesis, Random walk Model, Dynamic Gordon Growth Model, Empirical investigation of observed prices from the model with the application of cointegration theory.

 

Bibliography

Krause, A., 2001, An Overview of Asset Pricing Models.

Campbell, J. Y., Lo, A. W. and A. C MacKinlay, 1997, The Econometrics of Financial Markets, Princeton, NJ.

Campbell, J. Y./Shiller, R. J., 1988, Stock Prices, Earnings, and Expected Dividends, in

Journal of Finance, vol. 53, 661–676.

Campbell, J. Y., and R. J. Shiller, 1988, The Dividend-Price Ratio and Expectations of Future

Dividends and Discount Factors, Review of Financial Studies, vol. 1, 195–228.

 

2 Arbitrage pricing theory (APT): linear factor model and decomposition of asset’s risk premium (1 session)

« Exogenous » Factors associated with observed series according to Ross (1976) for theory and Chen, Roll and Ross, (1986) for empirical implementation.

 

Bibliography 

Chen, N.F., Roll, R., and S.A. Ross, 1986, Economic forces and the stock market, Journal of Business, 59, 383-403.

Fama, E. F. and K. R. French, 1992, The cross-section of expected stock returns, Journal of Finance, 47, 427-465.

Fama, E. F. and K. R. French, 1995 , Size and book-to-market factors in earnings and returns, Journal of Finance, p. 131-155

Roll, R. and S. A. Ross, 1980, An empirical investigation of the arbitrage pricing theory, Journal of Finance, 35, 1073-1103.

Ross, S.A., 1976, The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13, 341-366

 

3 Bond pricing (1 session)

 

-arbitrage free pricing of a bond: zero coupon and general bonds, interest rates and yield curves

- interpolation of yield curves

- factorial analysis of yield curves

- Back Propagation learning in neuronal network models: application to prediction of recessions by using yield curves

 

Bibliography

Cox, J. Ingersoll, J.E. and S.A. Ross,1985, A Theory of the Term Structure of Interest Rates, Econometrica 53:2.

Saaf, M. , 2000, Predicting Recession Using the Yield Curve: An Artificial Intelligence and Econometric Comparison, Eastern Economic Journal.

 

4 Pricing of derivatives in discrete time (1 session)

Uncertainty tree, binomial tree of Cox Ross and Rubinstein for pricing of call on a stock. Example of pricing of a call on corporate bond.

 

Bibliography

Cox, J., Ross, S. A. and M. Rubinstein, 1979, Option pricing: A simplified approach, Journal of Financial Economics. 7 (3): 229.
Implementation of the binomial model :

http://fedc.wiwi.hu- berlin.de/xplore/tutorials/xlghtmlnode63.html https://en.wikipedia.org/wiki/Binomial_options_pricing_model

 

5 Pricing in continuous time (1 session)

Introduction to diffusion processes, principles of derivation of Black and Scholes formula, simulation-based option pricing.

 

Bibliography

Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81 (3): 637–654.

Longstaff, F.A. and E.S. Schwartz, 2001, "Valuing American options by simulation: a simple least squares approach" Review of Financial Studies. 14: 113–148.

Heath, D. ,Jarrow, R. and A.Morton, 1992, Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation, Econometrica, Vol. 60, No. 1, pp 77-105.

 

6 Pricing of crypto-asset (1 session)

 

Bibliography

Burniske, C. “Cryptoasset Valuations”

Burniske, C. and J.Monegro, “Placeholder Thesis Summary”

D’Onorio Demeo, L. and C.Young « Valuing Crypto Assets “

Euler, T., “The Token Classification Framework”

Evans, A., “On Value, Velocity and Monetary Theory”

Gomez-Grassi, R.“Markowitz Portfolio Optimization for Cryptocurrencies in Catalyst”

Pfeffer, J., “An Institutional Investor’s Take on Crypto Assets”

Samani, K., “The Blockchain Token Velocity Problem”, “Understanding Token Velocity”

Srinivasan, B., “Thoughts on Tokens”

Srinivasan, B. and L.Lee, “Quantifying Decentralization”

Tomaino, N., “On Token Value”, “Our Process for Evaluating Tokens”

 

Student assessment: final exam (50%) + numerical implementation related to one of the topics of the course (50%)