Transform Analysis and Asset Pricing for Affine Jump-Diffusions

In the setting of affine' jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensityy-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option 'smirks' of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both amplitude as well as jump timing.

[1]  J. Gil-Pelaez.  Note on the inversion theorem , 1951 .

[2]  Shinzo Watanabe,et al.  Branching Processes with Immigration and Related Limit Theorems , 1971 .

[3]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[4]  M. David.  HARRISON, J. Michael, and KREPS, . Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory, , . , 1979 .

[5]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[6]  P. Bremaud,et al.  Point Processes and Queues: Martingale Dynamics (Springer Series in Statistics) , 1981 .

[7]  P. Brémaud.  Point Processes and Queues , 1981 .

[8]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

[9]  F. Jamshidian.  An Exact Bond Option Formula , 1989 .

[10]  P. Protter.  Stochastic integration and differential equations , 1990 .

[11]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[12]  Ren-Raw Chen,et al.  Maximum Likelihood Estimation for a Multifactor Equilibrium Model of the Term Structure of Interest Rates , 1993 .

[13]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[14]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[15]  S. Schaefer,et al.  Interest rate volatility and the shape of the term structure , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[16]  Louis O. Scott.  Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods , 1997 .

[17]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[18]  Ren-Raw Chen,et al.  Interest Rate Options in Multifactor Cox-Ingersoll-Ross Models of the Term Structure , 1995 .

[19]  D. Duffie,et al.  A Yield-factor Model of Interest Rates , 1996 .

[20]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[21]  Freddy Delbaen,et al.  No-arbitrage, change of measure and conditional Esscher transforms , 1996 .

[22]  D. Duffie,et al.  A YIELD-FACTOR MODEL OF INTEREST RATES , 1996 .

[23]  K. Singleton,et al.  Specification Analysis of Affine Term Structure Models , 1997 .

[24]  J.,et al.  Speci cation Analysis ofA ne Term Structure Models 1 , 1997 .

[25]  R. Jarrow,et al.  A Markov Model for the Term Structure of Credit Risk Spreads , 1997 .

[26]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[27]  David Lando,et al.  On cox processes and credit risky securities , 1998 .

[28]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options , 1998 .

[29]  E. Ghysels,et al.  Série Scientifique Scientific Series What Data Should Be Used to Price Options? What Data Should Be Used to Price Options? , 2022 .

[30]  D. Duffie,et al.  Modeling term structures of defaultable bonds , 1999 .

[31]  D. Madan,et al.  Spanning and Derivative-Security Valuation , 2000 .

[32]  Luis M. Viceira,et al.  Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets , 1999 .

[33]  Jun Pan.  Integrated Time-Series Analysis of Spot and Option Prices , 1999 .

[34]  George Tauchen,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999 .

[35]  E. Ghysels,et al.  A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation , 2000 .