| Home | Publications | Working Papers | Teaching | Talks | Personal | Links | |||
| Fall 2010, 1:30-3:30pm, Tuesdays |
|
Overview
The class starts by reviewing the basic properties of options and the first-generating option pricing methods such as the binominal tree and the Black-Merton-Scholes (BMS) model (as covered in Hull's book). Then, the class will discuss how to read information, and how to identify violations of the BMS assumptions from the options market. The final section of the class will go over some classic second-generation option pricing models, including the diffusion stochastic volatility model of Heston (1993) and the jump-diffusion model of Merton (1976). The class will end by highlighting the fact that most more advanced models are constructed by combining jump-diffusion return components (as in Merton) with stochastic volatility specifications (as in Heston).
Prerequisite Readings
Hull, Options, Futures, & Other Derivatives.
Modeling Financial Security Returns Using Lévy Processes. This handbook chapter explains the underlying ideas and reviews the relevant literature on option pricing with time changed Lévy processes.
Class outline
Class
Outline: A tentative list of topics per week.
Class Notes
Related Articles
Violations of BMS assumptions
Backus, Foresi, and Wu,
1997, Accounting
for Biases in Black-Scholes, wp. Carr and Wu,
2003, Finite
Moment Log Stable Process and Option Pricing, Journal of Finance, 58(2), 753--777. Bakshi, Kapadia, and Madan, 2003, Stock Return
Characteristics, Skew Laws, and Differential Pricing of
Individual Equity Options, Review of Financial
Studies, 16(1), 101--143. Wu,
2005, Crash-O-Phobia: A Domestic
Fear or a Worldwide Concern?, Journal of
Derivatives, 13(2), 8--21. Figlewski, 2009, Estimating
the Implied Risk Neutral Density for the U.S. Market Portfolio,
Volatility and Time Series Econometrics: Essays in Honor of Robert F.
Engle (Bollerslev, Russell and Watson, eds.). Oxford, UK: Oxford
University Press. Many useful details on how to process the index
options data to extract the density information. Option pricing using transform methods
Duffie, Pan, Singleton,
2000, Transform Analysis and Asset Pricing for Affine Jump Diffusions,
Econometrica, 68(6), 1343--1376. Carr and Madan,
1999, Option Valuation Using the Fast Fourier Transform,
Journal of Computational Finance, 2(4), 61--73. Lewis,
2000, A Simple Option Formula for General Jump-Diffusion and Other Exponential
Levy Processes, wp. Leippold and Wu,
2002, Asset pricing under the Quadratic Class, JFQA,
37(2), 271--295. Lee, 2004, Option pricing by transform methods: extensions, unification and error control, Journal of Computational Finance, 7(3), 51--86. Chourdakis, 2005, Option pricing using
fractional FFT, Journal of Computational Finance, 8(2), 1--18. Fang and Oosterlee, 2008, A novel pricing method for European options based
on Fourier-cosine series expansions, wp. Lévy (jump-diffusion) processes
Bertoin,
1996, Lévy Processes, Cambridge Sato,
1999, Lévy Processes and Infinitely Divisible Distributions,
Cambridge Merton,
1976, Option Pricing When Underlying Stock Returns Are Discontinuous,
Journal of Financial Economics, 3(1),125-144. Carr, Geman, Madan, Yor, 2002, The Fine Structure of Asset Returns: An
Empirical Investigation, Journal of Business,
75(2), 305--332. Wu, 2006,
Dampened Power Law: Reconciling the Tail Behavior of Financial
Security Returns, Journal of Business, 79(3), 1445--1474.
Stochastic volatility models
Hull and White, 1987, The
Pricing of Options on Assets with Stochastic Volatilities,
Journal of Finance, 42(2), 281--300. Heston, 1993, A Closed-Form
Solution for Options with Stochastic Volatility, with
Application to Bond and Currency Options, Review of
Financial Studies, 6(2), 327--343. Time-Changed Lévy processes--Combining jumps with stochastic
volatility (and higher moments)
Carr and Wu,
2004, Time-Changed
Lévy Processes and Option Pricing, Journal of Financial
Economics, 17(1), 113--141. Huang and Wu,
2004, Specification
Analysis of Option Pricing Models Based on Time-Changed Lévy Processes,
Journal of Finance, 59(3), 1405--1439. Research Area I: Specification analysis
Pan,
2000, The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study,
Journal of Financial Economics, 63(1), 3--50. Bates, 2000, Post-'87 Crash Fears in the S&P 500
Futures Option Market, Journal of Econometrics, 94(1),
181--238. Eraker,
2004, Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices,
Journal of Finance, 59(3), 1367--1404. Carr and Wu, 2007,
Stochastic Skew in Currency Options,
Journal of Financial Economics, 86(1), 213--247.
Wu, 2005, Variance
Dynamics: Joint Evidence from Options and High Frequency
Data, Journal of Econometrics, forthcoming.
Egloff, Leippold, Wu, The
Term Structure of Variance Swap Rates and Optimal Variance
Swap Investments, Journal of Financial and
Quantitative Analysis, forthcoming. Research Area II: Inferring
market price of risks from options data
Ait-Sahalia
and Lo, 1998, Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,
Journal of Finance, 53(2), 499--547. Jackwerth,
2000, Recovering Risk Aversion from Option Prices and Realized Returns, Review
of Financial Studies, 13(2), 433--451. Engle and
Rosenberg, 2002, Empirical Pricing Kernels, Journal of Financial
Economics, 64(3), 341--372. Bakshi
and Kapadia, 2003, Delta-Hedged Gains and the Negative Market Volatility
Risk Premium, Review of Financial Studies, 16(2), 527--566. Jackwerth
and Rubinstein, 2004, Recovering Probabilities and Risk Aversion from Option Prices and Realized
Returns, in: Essays in Honor of Fisher Black, editor: Bruce Lehmann,
Oxford University Press, Oxford. Bliss and
Panigirtzoglou, 2004, Option-Implied Risk Aversion Estimates, Journal
of Finance, 59(1), 407--446. Carr and Wu, 2009, Variance Risk Premiums,
Review of Financial Studies, 22(3), 1311-1341.
Bakshi, Carr, and Wu, 2008, Stochastic
Risk Premiums, Stochastic Skewness in Currency Options, and
Stochastic Discount Factors in International Economies,
Journal of Financial Economics, 87(1), 132-156. Mo and Wu, 2007,
International Capital Asset Pricing:
Evidence from Options,
Journal of Empirical Finance, 14(4), 465--498. Bakshi and Wu, The
Behavior of Risk and Market Prices of Risk over the Nasdaq
Bubble Period, Management
Science, forthcoming. Research Area III: Cross-market linkages
Carr and Wu, 2007, Theory and Evidence on the Dynamic
Interactions Between Sovereign Credit Default Swaps and Currency Options,
Journal of Banking and Finance, 31(8), 2383--2403.
Carr and Wu, Stock
Options and Credit Default Swaps: A Joint Framework for
Valuation and Estimation, Journal of Financial
Econometrics, forthcoming. Cremers, Driessen, and
Maenhout, 2008, Explaining the Level of Credit Spreads:
Option-implied Jump Risk Premia in a Firm Value Model,
Review of Financial Studies, 21(5), 2209-2242.
Carr and Wu, 2010, A
Simple Robust Link Between American Puts and Credit
Protection, Review of Financial Studies,
forthcoming. Research
Area IV: New specifications Carr and Wu, 2009, Leverage Effect,
Volatility Feedback, and Self-Exciting Market Disruptions:
Disentangling the Multi-Dimensional Variations in S&P 500
Index Options, separate modeling of asset value dynamics
and leverage variation. Calvet, Fisher, and Wu, Multifrequency Cascade Interest
Rate Dynamics and Dimension-Invariant Term Structures,
an extremely parsimonious way of modeling frequency
components in the term structure.
Some Useful References
Jean Jacod and Albert N. Shiryaev, 1987, Limit Theorems for Stochastic Processes, Springer-Verlag.
Uwe Kuchler and Michael Sorensen, 1997, Exponential Families of Stochastic Processes, Springer.
Philip Protter, 1990, Stochastic Integration and Differential Equations: A New Approach, Springer.
Stuart Alan and J. Keith Ord, 1987, Kendall's Advanced Theory of Statistics, 5th edition, Oxford University Press.
Dan Simon, 2006, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, John Wiley.